To me your post makes perfect sense. I went through that the last few weeks Dusty was with me. From what I've read on the net it's called 'pre-grieving'. And honestly getting through that time, horrible as it was, actually helped me somewhat with the grieving process after she died. At least while 'pre-grieving' you still have your pet with you and can do all those things for them that you might not have thought of until later when they were gone.

Hope that makes sense.

Don't fear so much you stop owning pets, just enjoy each day you have with them, pre-grieve now and again if you need to, and just love them for how ever long they have with you.