No self respecting kelpie will adversely affect its mode of transport. Kelpies LOVE travel by any motorised means. Mine will sit on the motorbike all day, or sail with me for a week, and she never gets in the way.
So CAR 256A (8) covers it - bugger asking CASA if it is only the dog and owner/pilot on board. Can you see the average cocky doing a stock or windmill inspection in his Drifter with his dog asking for written permission?. CASA would probably insist that the dog wear a hi vis vest, a hard hat and steel capped paw covers.
Forgiveness is often easier to seek than permission.
My only concern carrying well trained dogs in light sircraft would be the noise which could be a bit much for their sensitive hearing.