I like the eMedia Ukulele Method computer-based instruction. You can get a package with a ukulele for $60 at Guitar Center; I did a review
https://forum.ukuleleunderground.com/showthread.php?146782-eMedia-Mahogany-Ukulele-Pack-(EU08171)
Feel free to ask me questions about it. Although I reviewed the included ukulele poorly, it was compared to much more expensive instruments.
I've been teaching my son piano for the past 5 years. He has a private teacher, but I supplement it. There was a period of 6 months when I was his sole teacher, when he was between teachers. Based on this experience, I think the following are important:
1. Your daughter must want to play the ukulele (this shouldn't be too hard, she's only 7, you can manipulate her easily).
2. Play music that she likes. (e.g. is she into Disney's Frozen?)
3. Setup a regular teaching time (e.g. 30min on Monday 5PM)
4. Don't force her to practice; use a reward system (each minute of practice is 1 point)
5. Setup rewards for meeting goals (e.g. after passing a song she gets 10 points)
6. Have people listen to her (e.g. hold family music time where she/you perform for the family)
7. Never force her to like the ukulele. (e.g. if after a while she just doesn't like it anymore, you should just quit teaching her.)
IMHO, the ukulele is a hard instrument for kids (compared to, say, the piano or the recorder). My son was super excited about the ukulele but didn't like the pain from strumming or fretting. He's tried using a pick. I think the little fingers are just very tender. So he quit the ukulele after maybe 2 weeks. I only say this so that you don't feel bad if your daughter quits (I hope she stays onboard).