I don't think any answer except from your local code enforcement officer will matter.
My reading of the Florida code says ALL doors and windows that have an opening 42 or less inches above the floor have to be alarmed, or the pool has to have a barrier. The least restrictive condition for a barrier is a maximum sized opening of 4", and it just gets worse from there.
I think you would have to be able to show that no crawling baby could make it through the doggie door, and hope the inspector favors loose law interpretations.