I bought my daughter a Harley Benton CST-24 (PRS Custom 24 copy) and other than a bit of a dry fretboard I can't fault it. A bit of lemon oil on the fretboard and it plays lovely. Even the trem is decent and doesn't put it out of tune.
For the amp I bought a Roland cube 60 which has some great built-in effects. I wouldn't say the amp models sound exactly like a real valve amp but they're good enough for practice at home. The effects are decent enough as well. The 60 is really loud, a bit excessive for home practice maybe.
I'm looking for a guitar for child 2 now and possibly going Ibanez Gio and Orange Micro Terror as she likes that guitar look and the reviews for the Gio are great. The Terror amp is surprisingly decent, I've seen a band with one plugged in to a 4x12 and it sounded nasty.