I want, I want, I want... that's Veruca's motto. Something tells us she didn't want to be thrown down a garbage chute by a mass of squirrels, but, hey, who knows? From the beginning, Veruca is described as "a small girl […] who lived with her rich parents in a great city far away" (6.7). Most of what Veruca says and does revolves around the fact that she is greedy and wants everything she doesn't have. Her dad says that "'she would lie for hours on the floor, kicking and yelling in the most disturbing way'" until she got what she wanted (6.9). She sounds like a super fun person to have around.
She's the first to spot the Oompa-Loompas (and alerts the others with a shocking shriek [15.15]), but other than that, the only times she speaks are pretty much to say she wants something or to argue. And this is a girl who can't take no for an answer, so she has no intention of losing those arguments. In the end, that's probably her downfall – when Willy Wonka tells her she can't have a squirrel, she decides to take one herself. And as we know, things don't go well for greedy Veruca after that.
In the end, we find out she's a bad nut (24.34), but we can't blame only her. As the Oompa-Loompas point out in their song, her parents are at fault (25.67), because they've spoiled her rotten.