The SPCA I volunteered at allowed kids, but they had to have a parent with them. I'm sure every place is different, but if the better known shelters don't allow it (the pound, SPCA) look at more specific, smaller rescues. Like reptile rescues

Come to think of it, there is also a reptile club I belong too. We do tend to collect younger members who aren't allowed reptiles in the house yet, they come out and help us with educational events. If your kid is interested in any kind of animal, there is probably a club for it.