She is also hunted by the evil sorcerers who want to recruit and use her magic for their own purposes.
I think that the title of each book has something to do with a season or time of year.
At one point sometime after the dragon is hatched she is sent off to another world to attend a sort of dragon day care for several years. This world has separate time and the dragon returns fully grown shortly after she had left.
I also remember that the boy find a really weird looking stick and boasts about it a lot. Later in the series it turns out to be a relic of powerful magic accessible through dancing.
I read this series about 10 years ago.