Sorry not internetable, far too many variables. Certainly thousands of dollars. See if your realtor has a relationship with a good hvac company and they can come out to give you a solid quote for the work.

How old is the house? How old is the HVAC system? The duct system etc?

Most HVAC contractors aren't going to "touch" a system (to move it or whatever), then they get blamed when it doesn't work / and or if there are performance issues now --- that even you may not know fully yet.

These are the kinds of things that fall into the realm of "money is no object" meaning new system / bells whistles etc. OR you find someone desperate which in turn may make you desperate if they make a mess of your system. (air flow, mechanical and otherwise all these things play a part and even more so if you live in a more extreme climate -- Hot or Cold)

From the picture it doesn't look like the move is a big one, but a flat diagram just doesn't provide the detail that in person view would show.

Given that this is a new home (at least for you) it wouldn't be a bad idea, if you go thru with this purchase to begin your search for a trustworthy Licensed HVAC contractor in your area. (which is a mouthful these days -- for a variety of reasons -- the big one is that HVAC is in the cusp of going thru some dramatic changes.)

I service the Katy, Texas area.

I"ve moved both a couple of times during remodeling, got the gas meter moved outsde for free by the gas company as part of the last work. Because our equipment was old and inefficient we replaced it as part of the renovation/moving process. None of the companies who quoted the work batted an eye at the relocation part of the process. To move everything about 25 ft, gas fitting and plumbing ran probably $2K, duct work was within what might be expected for a new furnace/AC unit, all of the new equipment was sealed combustion so we didn't need to worry about reconnecting to the chimney (just as well, as the furnace flue was McGyvered into the wood fireplace flue, the joists were charred where they ran the flue pipes). Only regret is that we should have gone with a heat pump rather than a gas furnace. Upgrading to an on-demand water heater saved a lot of space. I thought it was going to be a big deal, it wasn't, and hugely improved the usefulness of the space.

Occasionally we'll need to relocate an air handler as part of a remodel. It's typically not a big deal and my HVAC trade partner doesn't get heartburn over it. I don't anticipate your rather short distance relocation will be problematic. That said, two points about relocating your home's air handler to the garage: 1.) ensure that the new location doesn't make the depth of the garage bay too shallow to accommodate a full-size vehicle, and 2.) make sure the system is well sealed to prevent introducing chemicals stored in the garage (gasoline, paints, insecticides, etc.) into the living area (which is why we prefer to not install them in garages) and well insulated to prevent condensation.

You're looking at $1000 to $1500 if it's just a furnace, twice that if you have AC along with it.