Dog door / flap fitted in to glass door.

If it's double glazed, then any glazing firm can quote. They will quote for a replacement sealed unit with the hole put in it. You will have to advise them of exactly which pet door you are buying/bought and at what height it needs to be from the bottom of the unit and whether centred ( best) or off centre.

Generally, you should not fit a pet door into single glazed door,
 
Generally, you should not fit a pet door into single glazed door,
Why not? It surely depends on the door? We have wood framed, hinged double doors from the kitchen into the garden. Each door has a single column of 4 single panes about a foot across and 15 inches high.
When we kept cats, I removed the lower left pane of glass, and cut a replacement pane out of plywood. I then set a rectangular plastic cat flap into the plywood.
Our cat came and went through the flap with no problem. The drawback was stray cats came in too and we eventually adopted one of them, a large tabby who had been ferral on the street.
We gave up keeping cats after our children left home and after the old cats died. So I removed the cat flap and re glazed that part of the kitchen door.
 
Why not? It surely depends on the door? We have wood framed, hinged double doors from the kitchen into the garden. Each door has a single column of 4 single panes about a foot across and 15 inches high.
When we kept cats, I removed the lower left pane of glass, and cut a replacement pane out of plywood. I then set a rectangular plastic cat flap into the plywood.
Our cat came and went through the flap with no problem. The drawback was stray cats came in too and we eventually adopted one of them, a large tabby who had been ferral on the street.
We gave up keeping cats after our children left home and after the old cats died. So I removed the cat flap and re glazed that part of the kitchen door.
You answered your own question, you removed glass and put in wood 😊
Door glass has to be toughened and/or laminated. You cannot cut into toughened glass, the likes of older laminated glass can be cut, but not easily, and tbh it will weaken the pane.
Cat flaps are usually for DGU's, I haven't seen one that wasn't, for yrs.
 
So the cat flap is in a square frame, circular/u shaped plastic flap, lockable. We had a bog standard square dog flap in the wooden back door, plastic flap, I advise rubber, our original two used to fly out and broke multiple flaps! Tricky to secure, tho.
 
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