OK, you should be a team, and pulling together to get stuff done, and this doesn't seem to have happened here, and that is contributing to your stress levels.
However, both you and DH are busy today. You both have a full days work to do, he also has to get the house ready for a viewing in addition to his days work. There's also a child to get dressed and drop to nursery, which it seems is something you normally do.
His day is busy and planned out, your day is busy and planned out. You overslept, meaning that your plans slipped and you were running late. Your expectation seems to be that the consequences of your oversleeping should be moved from you, to your DH, so that he picks up some of the tasks that it had been planned for you to do, whilst you carry on your day on time. He would be then running behind plan, because he'd taken on these additional tasks. If he has capacity to take on additional tasks, then of course he should do so. But if he doesn't surely it is the person who overslept who's day should be disrupted, not the day of the person who didn't oversleep?
I think there may well be a bigger issue for you to sort in terms of division of labour. When you're both working full time then night wakings/nursery drop offs/childcare and housework should all be shared out fairly between both of you.
As an aside, popping a baby back in their cot with some toys to play with while you get dressed is absolutely fine. They won't scream the house down, just play with the toys for a bit. You can chat along to them whilst you get dressed.