How old is she? Elementary school age? Teenager? Is she 'net-savvy enough to handle loading music onto her device with the usually crappy software that the music services make you use?
What kind of player did you get her?
All of the music services pretty much suck. None of them let you own your music - some are subscription services that let you eat all you want, but as soon as you stop paying the monthly bill, you have no music again.
The others are almost as bad, with DRM restrictions on where and how many times you can play the music you "buy."
eMusic has low-ish quality unrestricted MP3s, and they're not very expensive, but the selection tends towards the indie.
It also depends on HOW your daughter listens to music. Does she want just a song or two here and there from Top 40 hits, or does she tend to listen to whole albums? If it's the latter, it's cheaper to buy the CD and rip it. You get better quality that way, and you can sell the CD after ripping to lower the price some more.
So, given that, if you're willing to rent music for your daughter that will be tied to a specific device, then it's important to make sure that the device you bought will play the format of the service you like.
Y! Music is probably the cheapest out there, but the sound quality is like streaming music is. It's about AM radio quality. It's listenable, but not great. Oh, and that $5/month won't let you transfer songs to her MP3 player. That's just a come-on price. It's $119/year to sign up for Yahoo Music ToGo, and then 79 cents a track to "buy" (i.e. rent) the songs that can be copied to a Windows PlaysForSure player. And the list is
really short. Is the player you bought for her on that list?
The iPod won't play music from any store but the iTunes Music Store, which is one of the worst out there. Expensive, the quality sucks, and they limit you to moving the songs to 5 PCs, which sounds fine until you realise that's 5 PCs for the rest of your daughter's life. In other words, she'd have to re-buy her music in a few years of upgrade cycles.
You can get legal unrestricted MP3s from various Russian companies, since they have broadcast licensing fees for music over the internet (more like the fees radio stations pay labels, rather than the sales model) and I've used AllOfMP3.com now for over a year with much success. They have a download manager that's actually easier to use than iTunes, and they charge by the megabyte rather than by the song, and let you pick your encoding rate so that you can save money if 128kbps is good enough for your ears (I tend to get everything at 192kbps).
And the tracks you download from them are yours to keep and will play on any mp3 player, can be moved to unlimited devices or computers, you can back them up, you only have to pay once, etc.
Now is a good time to teach your daughter about the unethical practices of the current fair use restrictions placed on consumers. The record labels, aided by the government, want people to shift from buying things to leasing their use (essentially renting content) and they're hoping to indoctrinate your children in this way of unamerican thinking so they can make more money. Please note that the artists make less and less all the time. If you want to support an artist, go to their show and buy a t-shirt while you're there. They make far more profit from that than they do from their records.