They did not pay me for 4/1-4/8 - which within 30 days's notice

For rent, they will own me one week rent (4/1-4/8). If I have no one moved in, I am considering deducting 8 days rent from the security deposit. If I do have someone move in, I will deduct in according to how much days it is vacant.

I would like to know if it is all legal for what I am doing since this is the first time we ever rent out the house.