I only fed from one side for both kids until they were over one. I had frequent feeders though, with no break longer than 2-3 hours until they were almost 5-6 months. I would definitely wake such a young baby to feed. There is plenty of time for her to sleep longer. Right now she needs to be gaining weight and demanding your body make milk. It takes about three weeks for milk supply to be fully established.

Fluffing at the breast was generally a sign my babies wanted to suck but not get milk, such as being tired but already full.