You may prefer to just go through the wall next to the door. It would
be easier in some ways (no metal, no $500 door to ruin), but harder in
others (multiple layers of drywall, studs, sheathing, siding, etc.)

Keep in mind that a pet door weakens your security and unless you get
a "smart electronic door", you may be setting yourself up for unwanted
animals to get in your house. Beachcomber

I get a feral cat now and then, in through the cat door. I tried to adopt
them, but the resident cats (3) would not permit it, nor would the dog when
she was young.