Looking at the Forge spec. reminds me of looking at a BD spec... It's actually got a nicer drivetrain than my significantly more expensive Hardrock came with, but those hubs are total garbage.
OP, I don't know how good a price you came across on that Fox. Used ones sell for around $300 on EBay, depending on the specific model. I'd say if you're being offered a better price than that and you can afford to spend the money right now, don't mess around with intermediate upgrades - just do it. Run whatever goofy spacer stack above the stem you have to in order not to cut the steer tube if it's too long, stick a tennis ball on top, whatever. But you don't get a comparable fork on a new bike until you spend at least $2000 on it. Of the various bits and pieces I've bolted to various bikes over time, I'd say upgrading my suspension fork has been one of the ones that improved the actual riding part the most. It's going to matter less, I think, since you're starting with a Dart and not an RST, but gaining stiffness and tunability and losing as much weight as this part swap will lose will be pretty noticeable.
Check the manual (available on Fox's site) and make sure you can spacer it down to 100mm. While I wouldn't be too worried about a 20mm travel increase blowing up your frame, it will mess with the handling. Whether that's good or bad is pretty subjective, but you should have the option to keep the bike handling as intended.
There was one other technical question you asked - how to measure the height of your current steer tube. It's actually pretty simple. Measure from the top of the fork crown to the top of the stem or top spacer, and subtract 3mm. If the length is very close to the amount of remaining steer tube on the Fox and you don't have extra spacers under your stem, you might want to actually remove the stem, so you can see the top of the steer tube, and tap the fork down a little, so you can see the headset baseplate and get a more accurate measurement.
If ultimately you decide not to do it, you might consider getting the correct spring kit for your Dart, if you find you never use your full travel or it bottoms out a lot. That's one advantage their forks have over some of the competitors that are showing up from other brands lately.