Do I need a road bike?

[Owlie]

You can do a century on a hybrid/flat-bar road bike if you so choose. I would add bar-ends for extra hand positions and change out the tires for slicks if you haven't already. However, if you've got some money to burn, you might consider a road bike purchase. It's lighter and has "zoom" gears (but it won't make you faster!), though you lose some of the climbing gears. (I don't know how your Quick is geared.) If you go that route, I'd look for at least 105 components, possibly carbon frame depending on your budget and road surfaces.

Personally, I'd go with a road bike, because that really upright position probably wouldn't be super-comfy for a really long ride, but that's just me.