Tiny babies are the easiest to travel with, they don't do anything apart from eat, sleep and poo. I'd do a cottage no problem. If you're driving there maybe just plan a leisurely journey in case you have to stop to feed a lot.
DS is 5weeks, before he was born we considered booking a trip to Berlin for when he was 10 weeks. We didn't because we were worried about traveling with a baby. I really wish we had though, I think travelling with a teeny baby would be relatively easy.