My Eldest son got his first tooth at 12wks - it's more than possible - why not ask your health visitor to see if she can see any teeth cutting? (didn't mean to sound patronising then - you said you're a first time mum and might not know what the teeth coming through look like)
Try to give her teething rings to bite on, although at her age you will need to hold them in her mouth for her!! If she's hungry, she'll try to suck them, if it's her teeth she'll try to bite them.
And by the way, nothings wrong with her!!! and she's lucky to have a Mum as eager to help her as you!!