I wouldn't go with a Toys R' Us junker, because you're right, it'll probably not work right, and then she'll just get fed up with it. I've come across some really cheaply made acoustics where the tuning pegs had major issues that made it impossible to tune the guitar properly.
Guitar Center always seems to have some guitars for around $100 (even less) that would probably fit the bill. You might want to see about getting something that is 3/4 in size so its easier for her to fret as her hands are probably pretty small.
A couple of other possibilities are looking for something that might be cosmetically damaged, but fully functional, at a substantially reduced price, or buying used. Still, taking your daughter to the music store and finding a guitar for her might not be an experience to pass up lightly. If she sticks with it into adulthood, she'll probably always remember the day you bought her her first real guitar... your daughter, 20 years from now, interviewed by Guitar Player magazine: "...yeah, you know, there's a lot people that get to the where I am now, and they get caught up in the fame and glamour of it all... but for me, its all about the music. I still remember the day my Dad took me the the music store and bought me my first guitar. I was so excited! I get that same feeling now even after all these years.."
GP: "was that the guitar you used for the solo with Santana...?"
You get the idea... :)