I'm in the same boat as you, just a little further ahead.
You can swap just the gears without doing anything to the rear end, but you're really going to want some kind of limited slip in there so supply both wheels with traction. Ford trac-loc, as stlwagon said, is a popular choice.
The general consensus says to go with Ford Racing gears if you're going to do it. Other less expensive brands like Yukon, Motive, etc. will work, but are not recommended simply because they're cheaper.
Make sure you find a good shop with experience and who know what they're doing. A bad gear job can ruin your new gears, your new trac-loc, your new bearings and your rear end as well. A bad gear job can also result in howling and whining coming from the rear end.
Gears are something that you definitely want a professional to do.
__________________ Black 2005 Mustang v6, 5 speed, IUP, EUP and Leather.
Razzi 1/4 window scoops, Mustang GT Sway Bars, Flowmaster American Thunder Single Exhaust, Clear Front Turn Signal Lenses, Demolet CAI, X-cal2 91 tune, Hurst Comp/Plus Shifter, FRPP T-Lock, Ford 3.73 gears |