About halfway through the novel, we find out that Milly is the "dove" that Henry James is talking about in the title. We know this because Kate Croy says to her face, "[Y]ou're a dove" (126.96.36.199). What Kate means is that Milly is young, pure, innocent, and beautiful. Wherever Milly goes in Europe, she seems to be the most watched person in the room. As James' narrator tells us early on, "When Milly smiled it was a public event—when she didn't it was a chapter of history" (188.8.131.52). She is so young, beautiful, and rich (very, very rich) that people absolutely hang on her every word and gesture. This is a woman with so much to live for, but Henry "Dramatic Irony" James has her come down with an incurable case of T.B.
A dove is also a bird that people often keep caged in order to turn its beauty into private property. Milly figures out that her beauty has been privatized midway through the novel, when she realizes that old people like Susan Stringham and Maud Lowder are parading her around as if she's their possession. At this point, she recognizes the problem of being a dove: "That was what was the matter with her. She was a dove. Oh, wasn't she?" (184.108.40.206). At this point, Milly decides that she doesn't want to be a passive little dove anymore. She wants to be a confident woman who makes her own decisions. It's around this point that she also realizes that her illness is deadly (pun intended) serious.
When it comes to finding out about the details of her illness, Milly is her own woman. She even goes as far as lying to her friend Susan: telling her that she wants some time alone to go shopping in London and going instead to see a doctor. She finds a certain pleasure in deceiving her friend: "She found after this, for the day or two, more amusement than she had ventured to count on in the fact, if it were not a mere fancy, of deceiving Susie" (220.127.116.11). Here we can see Milly starting to enjoy her newfound sense of independence, and also her newfound ability to lie like a professional poker player.
Milly's sense of independence isn't just coming out of nowhere, though. It's important to remember that absolutely everyone in this girl's family has died out, leaving her the only surviving member. She more or less bases her identity on the fact that she's a survivor, saying, "I'm a survivor—a survivor of a general wreck. You see […] how that's to be taken into account—that everyone else has gone" (18.104.22.168). Milly isn't as delicate and frail as people make her out to be, and she's not as naïve. She's seen death firsthand. The great tragedy of this book, though, is that just as Milly starts to live for herself and find her independence, she needs to start preparing herself for death.
Early in her European trip with Susan, Milly seems to know that something is very wrong with her. She has visited a doctor in New York before leaving and her trip to Europe has been recommended to her as being (possibly) good for her health. On the surface, everything seems a-okay, but Milly has a sinking sensation that this will be her last trip ever.
When presented with a painting of a young woman who looks just like her, Milly can't help but burst into tears because the woman in the painting has been dead for a long time. And for Milly, it's impossible not to compare this fact to her own inevitable future: "And she [the woman in the painting] was dead, dead, dead. Milly recognized her exactly in words that had nothing to do with her. 'I shall never be better than this.'" (22.214.171.124). These final words are especially heartbreaking, since Milly knows that her health is about to rapidly decline, and that this will be one of the last times she ever feels healthy and well.
But, despite her terrible fate, Milly keeps her chin up and decides to face death by living the remainder of her life to the fullest. She tells her friend Susan as much when she says, "Since I've lived all these years as if I were dead, I shall die, no doubt, as if I were alive." (126.96.36.199). Milly has wasted much of her life letting other people tell her what to do. But if she's going to die, she wants to live and love on her terms while she can. And this is exactly what she does.