Rather than purchasing a cat door at a pet shop, and then arranging to have it installed by a glazier, hire the services of a glazier to supply and fit the cat door. You will find this will save you a lot of money.
Recently I have had to repair glass for three customers where they have been given bad advice. They were talked into cutting their own holes and sold a cheap glass cutter (not the right tool) and ended up cracking the glass. Beware of bad advice!!
I supply and fit standard cat doors for $95