If your dog weighs more than about 30 lbs I would look into a SOT with tank wells. Older Heritage and Ocean Kayaks that you can find second hand for not much money are great for this. My dog loved paddling on flat water but she hated rough seas. If you are a novice, stay close to shore with your dog until you have taken a few capsizes with him and know how he reacts when you need to deal with bad conditions.
