I've done a few sprint triathlons. You see everything from knobby tired mountain bikes to full fledged tri-bikes. You could do a lot worse than that Fuji. You'll be fine.

Have fun !

edit: Being that a sprint triathlon is a race you will see a ton of racing bikes. Don't let that psych you out. My brother has also done many tri's on a bike much like yours and he's relatively competitive. It wouldn't surprise me if he decided to get a road bike at some point but so far he doesn't felt that the one or two tri's he does a year is worth the expense of getting another bike.