Just a month? First, some providers wouldn't stop you right there, because that doesn't really give them a consistent income. and after you're gone will they be able to fill you spot immediately? Besides, if you do have 2 kids you may want to consider keeping you son involved partly so you have a little break and also for the social interaction.
Be sure to ask about sick policy? do you still pay for the day or can you accrue it?
Vacation days---either yours or theirs? Som e holidays you may pay for.
Early/late pick up/drop offs, penalties or policies.
How many kids vs. adults.
licensed/certified/registered with the state.
Ask if they have a packet of their policies. Generally, if someone has something in writing they can give you. The more organized they are and able to truly perform as a qualified daycare provider. They not just going day by day, sort of "address it as it goes".
We use one on a drop in basis. her packet was 15 pages long. which some may say very excessive, but it covered absolutely everything.
how do they determine meal plans. you want you child to get a balance diet, not eat cookies when there.
I am sure there are several other things someone else may say. But if they have a packet, take it home read through it, make notes, the answer to 1 questions may lead to another.