Bearded dragons don't have a very powerful bite. Their teeth are pretty small but are sharp, just not alot of jaw power behind them. I have been bitten by my dragon while it was young and again when fully grown. The adult bite is harder, but still not much more than a squeeze like pressure on the finger. A child may find it a bit more painfull than an adult and as their skin tends to be alot softer, the dragon may break the skin easier. But compared to bites from other lizards, bearded dragon bites are quite mild. Cats and dogs can do a much more painful bite, even when just playing and not trying to actually bite hard.
I don't recommend a blue tongue skink for a small child. THough these lizards are much more tolerent of handling and pretty docile, they do deliver a much harder bite than a bearded dragon. Their jaws are much stronger and they seem to hang on much longer than a bearded dragon would. I was bit by one of my blue tongue skinks while he was only about 6 months old. Not a bite out of aggression or fear, simply thought my finger was a nice big juicy silkworm and he probably would have let go right away if I pulled away. I was putting in his water dish, which is pretty heavy and I didn't want to let go of it in fear of having it fall on the skink and hurt him. So I let it bite till I put the water dish down and then moved my hand away. It hurt, not horribly so but deffinitely broke the skin and I could feel the strength of his jaws, even at that young age.
The other suggestions about proper hand washing and avoiding putting fingers into the mouth after handling a dragon, is very true and deffinitely should be followed. This precaution should be followed after handling of any pet, dogs and cats included. Salmonalla can be in or on any animal, not just reptiles.
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PHLdyPayne