Your baby sounds completely normal to me!
My DS only ever slept 40 mins at a time maybe 3 times per day at that age. Even now that's what he does.
Tell your MIL that your milk is all your DD needs. It frustrates me no end that others make new mums doubt themselves when it comes to breastfeeding. There is a booklet available through the ABA for grandparents that I wish I had bought for my own MIL.
Sounds to me like you're doing a fantastic job and your DD is thriving.