What is this small hole and why is it there at the bottom of sink?
This looks like it's tied into the overflow system for the sink. Your old drain pipe might have covered it up. If the old gasket will fit on the new drain pipe you could just reuse it or get a duplicate gasket from your plumbing supply store. I would hesitate to just plug up the hole because you never know when your plug would fail and you'd have a big leak. It could also compromise your overflow protection. You could also just put the old drain pipe back on the sink if you can't get a new exact match.