Can you say:
The rent was paid to December 1st.
Meaning we have to move out before that date.
The OP wanted to know if we can say
"The rent was paid to December 1st" under the condition that they move out before that date.
In actuality, if he/she were to move out before Dec 1st, their lease would have ended on November 30th (a normal end-date for a monthly lease-term agreement). It is the actual day on which the tenant must finish moving all personal property out of the apartment.
So, I proposed saying "The rent was paid
through November 30th" which is consistent with such an agreement. The vacancy statement is to assure the landlord that the apartment will be empty on December 1st.
I also suggested the second set of sentences, which more directly specifies the final move-out date of November 30th.
[additional information]
It is on December 1st that the landlord regains possession of the property and can legally enter the apartment without permission. In the laws of my state, any personal property left behind by the tenant still belong to the tenant for 30 days. If the tenant does not claim possession of said personal property within 30 days, the landlord takes possession of that personal property.