Darin,
I started my daughter out in a petzl Quissiti(sp?) kids harness. Its good for little ones as there are no buckles or anything in front where they can fidget with them. For rigging her up at first i just tied a figure 8 on a bight directly to the webbing loop on the harness. And at that young of an age, Id recommend belaying her from the ground. This way you can help pull her up when she cant quite make it on her own, and yet they stilll have the feeling of doing it themselves. Also at a young age advancing hitches is tough.
Basically just as you would recommend to a new climber..... start slow and low. Try to find a small tree with low branches in a park maybe?
My daughter started out in a small 6" diameter Red Maple that was no taller than 20-25 feet. I would hang a pulley up top, run the rope thru and terminate to her harness with the 8 on a bight and belay her from the other end. After the Maple became boring to her she graduated to a bit bigger tree, and Apple tree about 30 feet tall but a bit more difficult to climb.
Trust me she will let you know when the first smaller tree becomes boring and she's ready for something bigger.
Regarding harnesses, I would avoid a rock climbing harness as they are really not all that comfortable and really are designed to be sitting in. The petzl fids harness is a full body harness which gives some good security. In my avatar my girl is climbing in the new tribe kids saddle and she just got that in the summer of 06 at the age of 11.
She is now able to advance a blakes hitch, but needs the additional foot prussik to stand in when rope climbing.
Kids are actually amazing climbers, they no fear whatsoever, and do not want to stop climbing.
I say go for it, she will absolutly love it.