Handing over keys means deliver possession, it is a very serious matter. It means they can use the house now.
You have two choices
(1) not handing over key today
Sign a holding deposit today, with 1 month deposit. Holding deposit says you are holding this house for the teant until 11/1. Sign the full lease around 10/31, receive Nov. rent and give key. The 1 month holding deposit becomes security deposit.
(2) handing over key today
Sign the lease today and lease has to start today becuase you gave them the key. You can say you waived rent for Oct as bonus. They have to give you Nov. rent today.
(3) sign the lease today, taking deposit and not giving key is bad for the teant.
Sign the lease today, not taking deposit and not giving key is bad for you.