You shouldn't have hassles taking your pets into Moz, but please be aware that dogs or usually not kept as pets in rural areas, but for security and hunting and have to fend for themselves. You could be attacked by the local mongrels trying to get at your dogs if you are not careful.
Cycling in Moz is hard enough without the added concern of pets. Also to get your dogs back into SA you may have to see go through weeks of quarantine.
having said that many people take their dogs into Moz and back into SA with no problems all of the time.
Mike