Deb, unless I am missing something, the dad will have to file personal returns for both 2006 and 2007, and since he's not available to sign, I think you are correct to put date of death on top of both, and the personal rep or "person in charge of decedent's property" will then be able to sign.
You might check to see if he had savings bonds, because he can elect to report the accrued interest through the date of death on the final 1040. Might really save someone some money.
The estate, if even necessary (because of income received on probate assets after death), starts "at the moment of death", which is in 2007. I don't think you'll need to worry about that one. This is really interesting, and I hope others will add to this. I wish I knew more about it myself. I'm about to do a 1041 for a lawyer who died without a will. (?!!?) Has (had) about 35 investment accounts with no beneficiaries named on any of the accounts.
I am looking at The Tax Book section 21, and I think Pub 559 will help you, too. Sorry this is all I know at the moment. (Except that I am tired and grouchy.)