I know it is necessary to cohabit for 12 months before we make our application, but we will have been together for 11 months and 3 weeks when my visa expires. Will that be enough time for us?

The regulation defining Interdependency says you must have been in a "relationship" for a period of 12 months immediately preceding the date of application. This "relationship" includes financial, legal, social and domestic criteria and includes living together, or "...not living separately and apart on a permanent basis".

If you have known your partner for substantially longer than 12 months then it may be possible. However, people who met and formed a relationship within the 12 months would not be able to meet the requirements.