I don't think it is at all bad for a young child to learn how to treat animals with respect and care.
To be honest, this is your daughter and you have to do what you feel is right with regards to her. However there are people on here with hamsters and young children and I'm not aware of there being much of an issue with this.
Your hamster (what's her name?) is not a wild hamster, and there are no specific vaccines it is deemed necessary to give hamsters (unlike dogs, for example), so the risk of your hamster carrying anything that your daughter won't be exposed to in her every day living I would say is low. So long as you are keeping your hamster clean, well cared for, and attend the vets if anything is concerning I don't see why you can't continue to allow your daughter supervised access to your lovely sounding pet. Just remember that hamsters do have teeth and so you may want to make sure your hamster is as tame as possible before you allow your daughter to stroke (not that that guarantees anything!) There's great information on taming and other advice on here/on this site's wiki page.
Remember, young children get lots of coughs and colds and your daughter will need to stay away from your little hamster when this is the case as the hamster could catch a cold and become quite unwell!
Hope this helps,
Lydia and Artie.
NB: I am in no way an expert in this, I'm just trying to help you weigh things up - perhaps a vet might have a better idea as to the answer to your question.