A few taps with a rubber mallet is sometimes necessary to get the fork out. When you remove the stem KEEP THE FORK SUPPORTED!!! It can very easily fall out once nothing is holding it, even if it seems to be holding on its own.

If the bike that is getting the fork swapped to already has a 1 1/8th headset there is no reason to mess with the headsets really, provided they are in good condition. You will need to switch the crown races though, which CAN be done with a screwdriver but it chews up the crown and the race somewhat and I personally wouldn't do it.