Alice started to her feet, for it flashed across her mind that she had never before seen a rabbit with either a waistcoat-pocket, or a watch to take out of it, and, burning with curiosity, she ran across the field after it, and was just in time to see it pop down a large rabbit-hole under the hedge.
In another moment down went Alice after it, never once considering how in the world she was to get out again. (Wonderland 1.3-4)
Alice's first instinct when she sees something unusual is to chase it. She doesn't think about her own safety, she doesn't concoct a plan, and she doesn't feel scared. She just feels surprised, then curious, and we're off – knowing she's going to be a fun character to follow through the adventures she's certain to have with this attitude.
"Oh, Kitty, how nice it would be if we could only get through into Looking-glass House! I'm sure it's got, oh! such beautiful things in it! Let's pretend there's a way of getting through into it, somehow, Kitty. Let's pretend the glass has got all soft like gauze, so that we can get through. Why it's turning into a sort of mist now, I declare! It'll be easy enough to get through – " (Looking-Glass 1.12)
Alice moves rapidly from curiosity, to the desire to explore, to the ability to explore. Her imagination makes possible the exploration that she craves, even when it isn't logically possible.
Soon her eye fell on a little glass box that was lying under the table: she opened it, and found in it a very small cake, on which the words "EAT ME" were beautifully marked in currants. "Well, I'll eat it," said Alice, "and if it makes me grow larger, I can reach the key; and if it makes me grow smaller, I can creep under the door: so either way I'll get into the garden, and I don't care which happens!" (Wonderland 1.22)
Not only does Alice explore the fantasy realm of Wonderland, she also explores different states of being for herself. After all, that's what all children have to do – explore a new size and a new body pretty much every day.
Wonderland, Chapter 2
"It's no use talking about it," Alice said, looking up at the house and pretending it was arguing with her. "I'm not going in again yet. I know I should have to get through the Looking-glass again – back into the old room – and there'd be an end of all my adventures!"
So, resolutely turning her back upon the house, she set out once more down the path, determined to keep straight on till she got to the hill. (Looking-Glass 2.3-4)
Alice seems to have a sense that her time in the fantastic Looking-Glass World will be limited, and she's determined to explore as much as she can before she has to go home. This sense of limited time seems to imply that she won't always be able to imagine her way back there – this is a special, one-time-only adventure.
Wonderland, Chapter 3
Of course the first thing to do was to make a grand survey of the country she was going to travel through. "It's something very like learning geography," thought Alice, as she stood on tiptoe in hopes of being able to see a little further. "Principal rivers – there are none. Principal mountains – I'm on the only one, but I don't think it's got any name. Principal towns – why, what are those creatures, making honey down there? They can't be bees – nobody ever saw bees a mile off, you know – " and for some time she stood silent, watching one of them that was bustling about among the flowers, poking its proboscis into them, "just as if it was a regular bee," thought Alice. (Looking-Glass 3.1)
Once again, Alice's instinct to be businesslike and organized about the process of exploration is thwarted by the strangeness of the fantasy world. Like a good Victorian explorer, she begins to make a "grand survey" of the land around her, but she's quickly distracted by how strange the insects are.
She very soon came to an open field, with a wood on the other side of it: it looked much darker than the last wood, and Alice felt a little timid about going into it. However, on second thoughts, she made up her mind to go on: "for I certainly won't go back," she thought to herself, and this was the only way to the Eighth Square. (Looking-Glass 3.63)
The refusal to turn around gives Alice the courage to explore places that seem dark and threatening.
Wonderland, Chapter 4
"The first thing I've got to do," said Alice to herself, as she wandered about in the wood, "is to grow my right size again; and the second thing is to find my way into that lovely garden. I think that will be the best plan."
It sounded an excellent plan, no doubt, and very neatly and simply arranged: the only difficulty was, that she had not the smallest idea how to set about it. . . . (Wonderland 4.35-36)
Alice tries to set about her adventure in a businesslike, organized way, but it's simply not that kind of place. She's going to have to explore haphazardly, taking things as they come instead of trying to follow a prescribed path. There's a reason that it's impossible to make a map of Wonderland.
By this time she had found her way into a tidy little room with a table in the window, and on it (as she had hoped) a fan and two or three pairs of tiny white kid-gloves: she took up the fan and a pair of the gloves, and was just going to leave the room, when her eye fell upon a little bottle that stood near the looking-glass. There was no label this time with the words "DRINK ME," but nevertheless she uncorked it and put it to her lips. "I know something interesting is sure to happen," she said to herself, "whenever I eat or drink anything: so I'll just see what this bottle does." (Wonderland 4.5)
Alice's sense of adventure sometimes borders on the reckless. The author is careful to explain that Alice usually makes sure the things she eats and drinks aren't marked poison, but in this case she seems particularly careless. Isn't it likely that a bottle beside a mirror in a bedroom would be filled with cologne or some other toiletry that wouldn't be a good idea to drink?
Wonderland, Chapter 5
"I only hope the boat won't tipple over!" she said to herself. "Oh, what a lovely one! Only I couldn't quite reach it." And it certainly did seem a little provoking ("almost as if it happened to be on purpose," she thought) that, though she managed to pick plenty of beautiful rushes as the boat glided by, there was always a more lovely one that she couldn't reach.
"The prettiest are always further!" she said at last, with a sigh at the obstinacy of the rushes in growing so far off, as, with flushed cheeks and dripping hair and hands, she scrambled back into her place, and began to arrange her new-found treasures.
What mattered it to her just then that the rushes had begun to fade, and to lose all their scent and beauty, from the very moment that she picked them? Even real scented rushes, you know, last only a very little while – and these, being dream-rushes, melted away almost like snow, as they lay in heaps at her feet – but Alice hardly noticed this, there were so many other curious things to think about. (Looking-Glass 5.87-89)
It's not having but collecting the rushes that is important to Alice. In one sense, this is disheartening – she's just picking them for the fun of it and doesn't care about having them. But in another sense, what she values is the process of her adventure, not the end product or some souvenir.
Wonderland, Chapter 6
"Would you tell me, please, which way I ought to go from here?"
"That depends a good deal on where you want to get to," said the Cat.
"I don't much care where – " said Alice.
"Then it doesn't matter which way you go," said the Cat.
" – so long as I get somewhere," Alice added as an explanation.
"Oh, you're sure to do that," said the Cat, "if you only walk long enough." (Wonderland 6.45-50)
Alice has trouble accepting that everywhere could be somewhere. She thinks that she's open to exploring anything she comes across, but really she has expectations about what kind of place "somewhere" really is.