I was scrolling through and saw the word "dog."
Anyhow, we've had good luck with our Jack's Pack Cats (Jack's Plastic Welding <jpwinc.com>) rigged with a dog deck of PolyMax Kennel Flooring, STK# HA2215 or HA2217, 2' x4' panel @ $15.95 from <www.TekSupply.com> or 800-835-7877.
Our dog, Ruby, loves water and learned quickly to jump on the dog deck. It offers good footing and I've taken her through rapids (2+ or 3) with no troubles (she's got a PFD for that). If you bust a wave, the dog gets soaked: some dogs might freak and bail out, so beware. Anyhow, after a couple of calm-water floats, Ruby felt secure enough to lie down (see below).
This shows a half panel of PolyMax (24" x 24") rigged forward to the seat frame of the Pack Cat, with the edges laced through the grommet strips on top of the tubes. The rear is laced to a crosswise dowel and also to two dees that I added on the insides of the tubes (to keep them from twisting with the weight).
Ruby is happiest right behind the paddler, where she can sniff hair, lick ears, etc. It's also simpler to pull her out of the water than if the d-deck was way up front.
Here's a full panel and a cut half panel of PolyMax grid.
Besides rigging dog decks, it also makes good cataraft floors, with some structural support. Doesn't absorb water, resists UV, drains instantly.
No reason a dog couldn't ride in the back of a duckieľ the center of gravity would be lower. Not sure whether claws might ravage the fabric eventually. You could cut a piece of PolyMax grid, edge it with slit hose, and lace it down. But I'm a friend of Jack's and a longtime fan of Pack Cats, Fat Cats, and Cutthroats for exactly this sort of trip.
Ruby likes the setup enough that when I'm rigging, as soon as I get the d-deck in place, she jumps on and looks at me, as if to say: "Why so slow? Let's get on the water, boss."