It is ROUGH when your kids are so close in age. I wish I had a magic solution for you, but I don't. But, yes, I do think it is the first of many tough phases. Mine didn't bite -- they hit. When he was 15 months, my son starting hitting my daughter HARD over her head. Despite trying, we found there was very little discipline that has a significant impact on a 15 month old. Yet, I had to come down really, really hard on my 2 1/2 yr old daughter for the same behavior. This meant a really "serious" time-outs in which I separated her from the room we were in. With my consistent, serious disapproval (I looked deadly serious and spoke in a very cold, calm tone) and my immediate, consistent application of the "serious" consequence, she has stopped the hitting. (I'm still working with him.)
I do not agree with biting the child back, but that's just my personal opinion. I have always believed that my role is to model the appropriate behavior. But you'll need to do what's best for your family.
Because these close-in-age sibling problems never seen to go away, I've recently been given a suggestion to create a "private" area/corner for each child in the room where we spend most of our day. The other child is not allowed to enter the other child's private area. It should have a comfy chair and those special toys/things that the child is not willing/able to share. I have not tried this yet, but I know it would be perfect for my daughter. But, quite frankly, my son wants to be in his big sister's space (and use her toys) all the time...so I'm not sure how I can teach him to stay out of her area. I think it's a great idea, if you can execute it. Good luck and let me know how things go.