Thank you all for your input.
Our dog is a Doberman Pinscher and doesn't have any problems relieving himself on board - he is exceptionally well trained - so it's only really exercise that becomes an issue; he does need to let off steam! I guess he'd have to be happy with a swim on the longer passages and we'll make it up to him when we reach our destination.
The International Health Certificate seems like it could help out with some of the red-tape. We would be able to make the necessary arrangements prior to arriving in port; it's just one more thing to plan for. I guess the real obstacles are those places where bringing the dog ashore is out of the question. I agree Steve; it would not be fair to leave him on the boat in sight of land while we're away enjoying ourselves! So that means we either have to make the decision to not visit those places or not bring our dog with us on the trip
The more I think about it I'm sure my head knows the correct thing to do; now I have to convince my heart (and then my wife and child!)