Ok, basic research is done. The FT Super Bee speed build kit is here, six plugged rockets, a dozen igniters and a remote receiver switch are on the way.
Needs some fiddling with the transmitter programming, but I think I can have the arm switch on my radio, with the little girl having the ignition control after that.
Plan is to fly the model normally for a few minutes, with her having some sticktime, and as the battery drains down we'll arm the rocket and I'll see if I can keep it under control :-D