I'm looking for the title of a fantasy/scifi book.?

I red this book when I was a kid and I can't get it off my mind. It was abut a princess with long red hair and she wants to fight dragons. Then one day she gets singed by a dragon and she goes to this lake to heal where she meets a guy . Then she goes off to fight a big dragon and befriends a pack of wolves and bobcats. She defeats the dragon and then goes home to her kingdom which is conveniantly under attack, defeats them, and marries her cousin. But she always loved the man from he lake...

Can anyone help me?