There are a few red flags - particularly when you say he doesn’t really ask about you or your DC and only talks about himself. This is more significant IMO than what he said.
It does seem to have moved very quickly since May. I wouldn’t be too concerned but what he said in the absence of red flags like the above.
It was clumsily said, but clearly he is expressive in other ways and enthusiastic about wanting to spend time together. He obviously does have strong feelings for you and there is an intention on his part to continue to deepen the commitment.
I think if I had gone down the route of asking as you did, I would’ve pushed for more of an explanation at the time and not left it so open to interpretation and assumed the worst.
People have different ideas of love and it’s ambiguous what he understood by your question and what he meant by the answer. It obviously struck him as unexpected.
i wouldn’t assume he is using you for childcare based on your follow up explanation of why he asked you to stay with his DD, but you clearly don’t want to, so don’t. Tell him you want the day to yourself on Sunday to recharge.
I would pull back some more time for yourself and to reflect as there doesn’t seem much breathing space at the moment and it seems to be too much too soon.