Do I need to go for H1B Extension ?

My employer filed H1B for me and the same has been approved. The i797 says that the it is valid till 12/31/2012 since the SOW of the client is also ending by that date. Does that mean that I need to go for H1B extension after that period ? Whether my employer bear the cost for the same ?

I am assuming that if the SOW is extended, I can continue in the same project if I want to otherwise I can switch projects after the H1B extension. Please correct me if I am wrong.