What is this missing part called?

That's probably called a vent. The dealer's parts department will have a listing for it, but it will be a lot easier to just trot over the nearest salvage yard and pop one out of another car.

It looks like an aftermarket heads up display module.

Car stereo shops might have them. No idea on cost.

I've looked everywhere I can think of. The only thing I can tell is that it's either an inspection plate, which can be picked up a dealer or junkyard, or, as I said above, some sort of aftermarket heads up display mounting hole.

It's not showing up in any of the references as a vent cardiodoc.

Yup. After I posted that wondrous reply I noticed the vent is to the left behind the windshield. Chrysler never used that heads up display silly gimmick but some cars do have a "heat load" sensor that varies air conditioning output when the sun is shining on the driver's face. That is only used with the automatic temperature control system.

Due to the shape of the cutout and the tabs, it's going to be an original part, but the salvage yard will be the best bet for finding the right color replacement. You can also get an idea of what to look for by checking out other cars at used car lots, (or the Walmart parking lot)!

My picture is identifying it as just a plug.

Yeah, inspection plate. I thought that made more sense than aftermarket heads up display unit.

Good luck. Festive holidays.