Hamsters can be a bit skittish <sorry Jes....
> and especially with wee kids - can jump out of hands quickly and easily break their legs. We used to keep them at boarding school and we were 11 years old... they are cuddly when asleep but can run around pretty fast and disappear quickly if they are out of the cage.
I'm sure lots of little kiddies have them - but personally, I think 3 years old may be a little young for hamsters, wee hamsters are a little delicate - they can also have a nasty nibble - you know when you've been nipped! Obviously only my opinion. Fluffy hamsters may cause allergies too (like cat fluff). They don't live very long either, or so I believe (may be wrong on that completely). Gosh, I sound like I am against them, really, I'm not, just ..... well... that's my experience.
Maybe Pdawg will be along and can advise about the age appropriateness for hammies.
Guinea Pigs are a lot more resilient with kiddies - and not so furry as opposed to wiry hair - and can be awfully cute too - easier to handle and slower if running around outside in an enclosed garden. Our friends had them for their kids and the kids were great with them when they were little.
Good luck hun - kids having pets is wonderful.