[Ironlight]

I think there are multiple interpretations of what you are stating your issue is in the responses thus far. Let's be clear about what your stated problem is: There is a gap between the bottom of the door jamb (ie the left and right inside faces of the door frame) and the floor. Correct? If not, then you're not talking about the jamb, you're talking about a different part of the doorway.

If that is your problem, I would cut a piece of 1x4" to fit, or whatever the correct dimensional lumber is, slip it in, glue, fill, sand and paint. Or just fill entirely with decent wood putty although in that spot it solid wood would be more durable.

 

[Ironlight]

Beat me over the head if I'm stating the obvious, but for one room, I'd invest in a few sheets of AC plywood for underlayment.

Maybe I'm missing something, but for about 100 bucks, the floor can be brought up to the proper height and you will walk away with a professional looking installation.

The floor outside the room should be at the desired height already. Bring the plank floor up to match.

If I'm not mistaken the problem is that someone made hash of the carpet installation, doing stupid stuff like cutting the jambs. I don't think he needs to raise the floor because it's already at the right height relative to the rest of the house, but rather repair the trim around the perimeter which was butchered when the carpet was installed.

Then again these things often come down to a judgement call of effort relative to cost and result. You may be right that additional subflooring will give the best result, finish wise, relative to cost and effort. It's either raise the floor or lower/repair the trim.