The bottom line here is that he cannot force you to go shopping when you are wiped out. If he thinks he can, your marriage is in desperately bad shape.
I can also see why he doesn’t want to take her shopping on his own; it’s very stressful shopping with a newborn who’s likely to wake up and start screaming the place down at any minute, and if she’s in that zone at the moment, neither of you should be putting yourselves through that, if there are any alternatives - and there are.
As others have said, there are solutions. He does the shop on his own on the way home. You get an online delivery tomorrow. The problem seems to be his fixation on “making the most of” the time you have together, even if what you’re doing is going to make you all extremely miserable.
He needs to understand that routines sometimes have to change with a very young baby. He needs to understand that doing something that’s just too much for you is not “making the most of” the limited time you have together. He also needs to understand that he does not have the right to insist on you doing something you’re really not up to doing, and which could be avoided. He doesn’t get to make your decisions for you. That veers into controlling, abusive territory.
Tell him you don’t care if he does the shop on his own, or with DD, or not at all because you’ll get a delivery tomorrow instead, but the one thing that is certain is that you are not going shopping today. If he doesn’t accept that... you have a problem.