It depends on your motivation and how far into your training you are. I'm presuming you've not done regular 8- 10K runs immediately prior to starting your training programme.
If you haven't been that regular 10K runner, and if your motivation for the race is just to finish, then consider sticking to 11 miles max as you suggest. Perhaps next weekend (then start tailing off the maximum distances in the following weeks as you approach the race - but keep up the regular runs - including a bit of interval training/speed work/cross training... I presume you've read advice on training programmes somewhere on the internet or in a book.)
If you've got the ambition not just to finish, but secretly also want to achieve a time that makes people say "wow", then I'd suggest that you run the full 13 miles this weekend (probably a 45 second per mile slower than the pace you've been running for the first 12 miles.... then give what you have left for the last mile ). Then you know you've got the distance in your legs. Then make sure you include a bit of speed work (e.g. a pacier 10K, and/or some interval training) perhaps 3 or 4 times over the following 2 weeks. You'll know that the last week before the race should be relatively gentle.
Good luck and enjoy it!
Edited: 02/08/2012 at 06:22