don't know about a doggie door that would work into a glass sliding door but i like to WARN you for one thing!!!!!
I don;t know where you live and what the local building codes are but in some areas/countries they require tempered glass in sliding doors ,do NOT try to cut this this glass!!!!It might EXPLODE on you!!!
i work with glass and get sometimes people asking me to re size a glass door or a glass table top.. if i even think it's tempered i don't touch it!