The jump won't be anywhere near that big based on bike alone. Two things about mountain bikes really slow people down, aerodynamics and rolling resistance.

At 9mph, the aero resistance is minimal. Rolling resistance is going to be noticeable, but even that won't be insane. I'd guess you may pick up 2mph, but I'd guess you could get that simply by putting more air in your tires. Most n00bs ride with their tire pressures way too low.

What's holding you back more than the bike is your physical condition, so if you just ride more, you'll speed up fast. The faster you go, the more difference you'll notice between a road bike and an MTB. Since you want to do this triathalon in the summer, I'd guess that you could probably get in good enough shape to do the cycling part at 15mph or maybe a little higher on a road bike, probably closer to 13mph if you stick with the MTB.