That sounds pretty good! Probably supply isn't her problem at all. If that's what she needs to do to get through, then that's what she needs to do I hope things settle down for her soon.

Absolutely bed-sharing/co-sleeping is a great way to get more sleep. There's an article she can download from the ABA HERE. It certainly can be done safely in most circumstances. She might even be able to move her cot/bassinet up next to her bed? I have the cot side-car style and that gives us a bit more sleeping space.

Does she have a sling?

It certainly does sound like she's doing a great job!