It is best to have 11 weeks as then it is possible to arrange things so that every possible pair of players occur together on the same team exactly 5 times.
(H C B L F D) v (K E A G J I)
(C H B K G E) v (L A F D J I)
(L D I K H G) v (A B C F E J)
(B I J C L K) v (F G H A D E)
(C D G I B A) v (F J E H K L)
(A J K B H D) v (E G L C I F)
(H F A I K C) v (J L E D B G)
(I A H B E L) v (D C K J G F)
(G B J F I H) v (E K D L A C)
(I E C J D H) v (K F G A L B)
(J H L G C A) v (D K I E F B)
Above the players are also arranged so that the same player never occurs more than twice in the 6 positions (1 2 3 4 5 6) on a team. I guess you could use this feature if you wanted to try out every player in every position.
If you need a 12th week then you can use any assigment of the 12 players to 2 teams of 6.
The schedule above is an example of a resolvable incomplete block design for example see here (http://mathworld.wolfram.com/BlockDesign.html)
Hope that helps.