Gabardine is a type of weave, not a type of fiber. If it's wool you'll need to dry clean. Actually, since it sounds like the suit is already made, you'll probably want to dry clean it anyway, especially if it's lined, tailored, got shoulder pads, anything like that-- because you don't know what the materials are, whether they were pre-washed, and whether they're going to shrink. If the fabric shrinks and the lining doesn't, or vice versa, or the thread shrinks, or you name it, the piece is going to be ruined. If it fits like a glove now, I wouldn't want to take any chances with any possibility of shrinking.
If you just have a little time between the two events, you might just hang it up, spritz it with Febreze, and iron.