Can there be dollar version of bitcoin? Why can't there be a p2p software that works like bitcoin but you load it with dollars?  

Can't something be made that's just p2p dollar transfers and not deal with a speculative new currency and its volatility?
That would be absolutely possible. In fact, there is a cryptocurrency out there called "Hashdollar" which is trying just that. I didn't look into it yet but if you tie the value of the Hashdollar to the US Dollar, you could use the p2p network to make "real" dollar transaction. The problem here is though, who will guarantee for the value of the Hashdollar? The value of Bitcoin is mostly made by market mechanisms but if you tie the value of a crypto currency to the dollar, you would need to have some authority to guarantee for that value and I do not see that happening. 

Of course the feds could just come up with their own version of a cryptocurrency (eDollar?) and this might actually happen very soon.

Hashdollar: https://bitcointalk.org/index.php?topic=368237.20