It occurs to me that I've read at least two stories about downtrodden young boys (slaves/servants) stealing a dragon egg for their own and rising to prominence. (There's also a Pern short story about an unexpected runty little dragonboy, but there was no theft involved nor scheming intent on his part. It just happened to him, there was no plan. Then there's Eragon, but I haven't *read* that and don't intend to.)
But I can't immediately think of stories involving a *girl* stealing a dragon's egg. (Menolly sort of?)
I do know of one where three children steal an egg together, two boys and one girl, but it's still one of the boys who gets the dragon.
In settings where you don't typically have girls as fighters, it seems like "Okay, I get BIG weapon that flies and breathes fire on you! I will nurture it and train it to love only me!" is a logical plan. Hmmm...