If I buy an unlocked blackjack, can I just use the Cingular(AT&T) sim card from my Razr and have it work fine?

Im looking at upgrading my phone since I have the V3 Razr which has alot of problems. If I take it to the AT&T store they will just give me the same phone and I really don't want to deal with the problems all over again. So I'm looking at buying an unlocked Black ebay and was wondering if I could just take the sim card out of my Razr and just put it into the Blackjack. Would everything work? Would I have to change my plan? Any help would be greatly appreciated. Thanks!!