Would a carbon fiber fork make a significant difference?
No, it is not a good upgrade.

The fork change could save some weight, up to about 400 grams. This is less than difference between full and empty bottle. The ride quality may or may not change depending on your current fork and the replacement. 

If you can't look up the specs of your bike, you can always measure yourself, the critical measurements are steerer tube diameter, steerer tube length (new forks come with extra and you are supposed to cut them, just don't get too short one) and distance from fork crown to axle.