You should be able to get a uPVC infill panel to replace the glazed panel that you have now. Once you have fitted this you should be able to make a cut out to fit a dog door.
Bear in mind that as you are in a rented property the landlord might not be happy with you altering the door, although if you can keep the glazed panel you should be able to replace it when you leave the property.
the glass panel should be held in with beading around the glass on the internal side of the door. this beading clips in and needs to be prised off. then the panel should just fall out (are you ready grandad?)
be aware that the beading can become brittle and break when you try to take it out. as you are likely to need to keep it to put the upvc panel in the go carefully. you may find it difficult to replace if it does break.