Yeah you can put the new sim card that comes in phone in your father's phone when it arrives. Then put your old sim card in the new phone.
If the sim cars are wrong sizes, you can use size adapters or call ATT before turning the phone on and they will sometimes swap it around for you (what sims go with what). Or as another person said, take it to AT&T store for correct size sims.
Note, at lease these things worked for me in the past, no guarantee things haven't changed.
However, I recommend Apple.com instead of AT&T website as the return policy is better if something goes bad, damaged phone or you don't like the phone, etc.