Yes, the sheetrock will be much thicker than wood paneling, and so you need to widen the door frame in order to install the frame around that door properly.
Probably the easiest way to do that is by simply having some clear fir 2X4 material cut into the width you need on each side of the door jamb, and then predrill and nail your door frame to that added piece of wood. If your door jamb is stained and varnished, then you'll want to match the stain, too. I would probably just glue those strips in place to the original door jamb with either white wood glue or construction adhesive.
NOW, I didn't read this whole thread, but I did notice some things I thought I should comment on:
The way people typically install drywall when renovating a basement is really dumb because they do it the same way as professionals do, and the pro won't spend so much as 5 minutes or $5 more to make the job much better at handling a sewer back up or small scale basement flood.
Here's the better way:
1. Decide on the baseboard you're wanting to install. In this particular situaiton, where you're designing against an accidental flood in the basement, the wider the better.
2. Now, have some 1/2 inch construction grade spruce plywood ripped into pieces a little narrower than your baseboard. The reason you want to use construction grade spruce is that "Good 1 Side" fir plywood will be sanded on the good side, and that makes it a bit thinner than 1/2 inch. Construction grade spruce should be exactly 1/2 inch thick, just like drywall.
3. Nail the spruce strips to the bottom plate of your wall, measure from ceiling to top of spruce strip, mark your drywall and cut, set the drywall on the spruce strip and screw it to the studs.
4. Mud your joints and screw heads, put on your corner beads and when dry, hold a bright light close to the wall to make any rough spots easy to find. Scrape off anything that's sticking out with a tungsten carbide paint scraper. Unlike sanding, scraping creates large pieces of gypsum that fall to the floor instead of hanging in the air so you're not inhaling any gypsum dust.
5. When you're finished sanding, priming and painting, put your baseboards on. Since they're wider than the spruce strips, they cover the spruce strip entirely, and he installation looks identical to the conventional way of installing drywall...
A) Now, your basement walls are water proof up to the elevation of the top of those spruce strips. So, if your sewer backs up, or you get really hammered and knock over a big aquarium, or you make your own beer and you drop a 5 gallon glass carboy on the concrete basement floor, or your basement toilet bowl overflows then you may have wrecked the carpet, but the walls won't need any work.
B) Now, you have solid wood behind the baseboard, ergo you don't have to use longer (pronounced "thicker") nails to put your baseboard on. So it makes it easier to both install and remove your baseboard those times when you want to replace your flooring.
This is how I rebuilt the bottoms of the walls in my sister's house after a super heavy rain caused her basement floor drain to back up and flood her basement.
And, most people aren't aware that Georgia Pacific "DensShield" which is a gypsum based water proof board is also available in 4 foot by 8 foot by 1/2 inch thick sheets. So, if you really wanna design against the Mother of all Sewer Backups, you can install your drywall horizontally and use DensShield for the bottom course. 4X8 sheets cost about $50 each here in Winnipeg about 10 years ago.