Marriott will automatically reset your 'nights counter' at January 1.

However, I was in the same position last year - joined in October, and after sending a note to the elite guest service desk they confirmed I would be able to use a 'rolling 12 months' in my first year of membership "as an exception", though I did have to monitor this myself and let them know so they could upgrade my status in their system manually.

i.e. I had 19 nights between October and January 1st and after 31 nights in 2003 I got back to them and was upgraded to gold. After 56 I got back to them again and was upgraded to platinum. At that point the 56 nights was being counted afresh towards 2004 status.