I don't have a child but I do teach lessons to kids.
I have one rather "horse-smart" ten year old that I allow to lunge Lacey. I never leave her alone while she's lunging and so far we've just kept it walk/trot on the line. I feel like, even though my mare isn't likely to kick out or buck at the canter, things are easier to keep under control when cantering is not there.
I stand close by but not inside the circle while she lunges - that way I can easily step in if I'm needed. I do find that my mare is mildly distracted by my presence but whenever she gets distracted I have my lesson kid do a lot of changes of direction, stops, etc, which underlines that Lacey should be listening to the kid, not me.
I'd say that if your horse knows what lunging is, lunges well (no excessive pulling, no bucking/kicking out, no bolting, etc), and YOU feel comfortable, go for it! However, if you feel uncomfortable, there are a bunch of other things she can do that are probably better groundwork than lunging is (leading over/through scary objects, etc).
And there's always the walking option. She doesn't have to trot or canter the horse on the line, especially at first.
Fabio - 13 year old Arab/QH gelding
Hazel - 14 year old Angora goat
Atticus - 4 year old LaMancha/Alpine cross goat
Rest peacefully, Lacey.
Last edited by Wallaby; 09-19-2012 at 12:07 PM.