My approach is a little different. My son plays piano. He's 7 and this is his second year. My daughter is eager to start, but I told her she has to wait until she's 6 as well.
I told my son that he doesn't have a choice about playing piano and he'll be taking lessons until he's 18. I don't know if I'll stick to this statement or not, but it doesn't give him a way out. Plus, I think there are so many benefits to learning to play music, not just artistically, but mathmatically as well. I treat it just like the requirement to go to school. In fact, many schools have taken music out of the curriculum and it's unfortunate because of all it has to offer. I'm not interested in my kids becoming masters/professionals/prodigies. I want them to learn the basic skills, give them opportunties for artistic expression, and grow academically. It's like learning another language and now is the time to teach that so the information sits in the part of the brain that makes it natural.
My approach is...I found a teacher who does not pressure and makes it fun. My son LOVES going to his lessons because his teacher is so nice. But, he hates practicing (just like he hates homework). His teacher and I have taken his lessons very slow intentionally so practicing is minimal (he practices for maybe 10-15 minutes a day). He has the ability to advance faster, but why? I want it to be fun and not a burden (just like school). It's about the creating the habit of practicing and teaching those fingers to move. I try to minimize the stress as much as possible.
My son also earns rewards for achieving certain goals. In the beginning, he earned rewards just for practicing everyday. He would get a star in his practice book for each day he practiced and on lesson day we'd go out afterwards for ice cream if he practiced everyday.
I agree that playing an actual song would make it more fun. My son loves hearing his sons come together. He can care less about his scales (unless that's one of the goals I set for him with a reward waiting), but a song makes it all come alive.
We also don't do recitals as that's more stress than what my son wants. I have mixed feelings about this, but I figure I'll know when the time is right for him to perform. Again, my goal is not for him to be a performer, but to earn great skills. When he gets into third grade, opportunities for him to learn other instruments will be offered at school. If he wants to learn other instruments, then I will let him. But, for me, piano will still be a constant. And, so far, he doesn't hate me for it (like another poster said).
Another thought...with piano, there are schools that do group lessons. Yamaha School of Music is one of them. I decided not to go with the group lessons for my son because he gets distracted easily, but I've heard wonderful things about this approach. Sometimes having a friend who's doing the same thing and could spark friendly competition is a motivator. I think Yamaha teaches violin as well. It might be something to think about that might work for your DD.