There are many variables that would influence how you transport your dog. The breed, size, temperament, and training will make certain choices better than others. I often take my dog, a black lab who weights about 70 lbs, with me in my kayak, my canoe, and small boat. She is enthusiastic, but also very well trained. This means I can ask her to sit up in the bow of the boat, the first seat in our two-seater kayak, or down on the floor of the canoe and she will stay there, mostly. She doesn't need a PFD because she swims much better in current without one than with one. On cold days, I sometimes give her a neoprene jacket that helps a little with buoyancy, but also keeps her warm. I sometimes take her just because the boat rides better with her on the bow, so I definitely encourage you to give it a try.
Because she is exciteable, I have to be ready for unexpected shifts. Usually this is no problem, but I never place anything on the deck that can slide off, and I always have the gear ready for a cold-water experience (I am most often out in the winter, as we are usually duck hunting together on a river). A more stable kayak with pontoons is my favorite, but the advantage of a canoe is that when she lays down, she can't see quite as much to get excited about and will ride a little better.
If you have a small dog, your lap may be better with a PFD, or if you have a large dog who is less likely to listen, you might want to skip it all together. With small dogs, get the PFD with the handle on the back so you can pluck them out. And remember, dogs can usually swim, don't wear clothes or shoes, and are generally bad-assed. A friend of mine drown while trying to rescue his two dogs who went overboard, leaving his young son adrift in the boat. The dogs swam to shore just fine, and other fishermen found his son. Stay in the boat and let the dog find her way to safety if there is an emergency.
If your larger dog goes in the water, one important trick to know is how to load the dog back into the boat. The technique is specific and non-intuitive. As your dog approaches the boat, you scoot to the other side to counterbalance. Now, as your dog's paws start scrabbling at the side of the boat, reach around behind her head and cup the back of her head. Pull her head towards you. This will allow her paws to get a purchase on the gunwale or side of the kayak and pull herself into the boat. You can't usually lift very well without tipping yourself, and the dog has plenty of strength to climb in if they can get a purchase, so concentrate on giving them traction rather than lifting. Once the dog's head pops up, reach with your other hand to grab her collar and pull/lift her towards you to take a little more weight off. I practiced this technique on warm days when I didn't have anything other than me and the dog in the boat, and now I do it all the time when she goes in the water for a retrieve. With a little practice, it becomes second nature to you and the dog.