Thank you so much for your answer. I checked my LCA, I129S and everywhere my employer had mentioned 3 years as my project duration.
I also talked to my employer and they said not to worry about as they will file for the extension once I will be there. Even they also did not look at the date in my I797B. And even if they had seen it, they couldn’t have done anything as it is not under their control. The problem that my parents saw the date on visa stamp and they were kind of worried as it mentioned 1 year only. Going to USA is big decision for me and my family. I am leaving behind good job. So from that point of view their concerns are also valid.
I still though have couple of more concerns.
1.) How hard is to get H1B extension?
2.) Say I travel to USA in December, 2012 and as my I797B has date upto Sept,2013, it is more likely that I will get same date on my I94. So when I will go to DMV for my driving license, I will get license upto sept 2013. Now, say my H1B extension gets approved then how should I get extension in my driving license? This is very important I will be having my family there (my wife and my kid). Please try to answer me this question if you have any knowledge.