I would absolutely recommend Leafy Town Pad. We stayed for nine days and it was the perfect base for a Hobart holiday with our eight-month-old. We loved the bread baking when we arrived and there were plenty of homely touches around the place to make it a comfortable stay. With the fire, heaters and hot water bottles we were warm enough despite the cold weather and having a fully equipped kitchen and washing machine we had everything we needed for a long-ish stay with a baby. And Nina even provided the portacot! Nina was a very caring and attentive host.
I would recommend having a car for the stay there as it's a half hour walk to town and the buses aren't all that frequent, but it's not essential.
All round a great place to stay.