Replacing a door's glass panel with a wood panel
I would suggest a quick visit to any building supply recycling type place near you to see if you can simply grab an inexpensive replacement door that's already better suited to installing a pet-door in - you may have structural issues with this door if you cut away a significant part of the bottom to insert a pet door. Replacing glass panels with wood is not the same (structurally) as a solid wood door (or door with glass on top and a solid wood bottom.)

Even if you have to buy it new, it would be a lot less work and more dependable to use a different door here.