Any items intended for children and babies must have permanent labels attached, with very specific information included, due to CPSIA regulations. Check out this Etsy team for info:
http://www.etsy.com/teams/6861/keeping-up-with-cpsia?ref=pr_teamsAs far as brand tags go, I don't think most people mind having a tag on a handmade item (my tags say "Handmade" on them, among other things), and another thing to think about is that, if they want to buy from you again, or if a friend asks where they got that adorable bib, they'll probably look for a tag to remember your shop name. If all they can remember is "I got it on Etsy," it's not as likely to give you repeat/referral business.
So, yes! Tags and labels are a good idea!