If you feel the need for a 3/4 size and decide to go with an electric (that's what the kid really wants, right?) your choices in terms of real musical instruments are limited.
While I generally prefer Fenders over Ibanez, in the world of mini-electrics, I think the
Ibanez Mikro is tough to beat. The two I've played were surprisingly decent, played easily, stayed in tune, and actually sounded musical...
The

Squier Mini-Strat is cute, but is useless as a musical instrument unless you
upgrade the tuners, an added $30-$40 expense, plus the price of installing the new tuners if you can't do it yourself. Even after upgrading the tuners, the electronics are marginal at best.
The
Jay Turser Mini Strat is similar to the Squier Mini, but with better quality tuners already installed from the factory. I haven't played one yet, but it looks promising.
With an electric, I'd also recommend getting an entire box (10 sets) of 8-38 ultra light strings to go with the guitar, along with a dozen extra high E strings...
