Our DD was like that, more so during the day though, and at her first weigh in with the MCHN about 2 weeks after leaving hospital, we found she'd only gained 60g So, from my experience, I'd be inclined to wake her at least throughout the day to ensure she's really getting enough to eat.

Our DD was little (6lb 8oz) and a very sleepy baby. We had a lot of BF issues because of this and we had to wake her for feeds until she was 6 or so weeks plus give her top ups (EBM) after every feed until she grew strong enough to wake and feed properly on her own. I was expressing around the clock, the whole experience was very stressful.

Sorry, don't want to scare you but I had to share my experience with a sleepy baby. Just a few things to think about.