No, it does not have to be a dell branded battery, however, it does need to be specifically made for that laptop. Here's one I found:
http://www.ebuybatteries.com/product/laptop_batteries/Dell/Dell-I-312-0428.htmIt's the same capacity as the one you have. I checked their reseller rating, and they're legit.
I would seriously avoid buying one from eBay. There is so much counterfeit and fraudulent electronics on eBay that you just can't trust them anymore.