Check out the WS Tarpon 140
Our dogs (Shelties)usually go on our numerous camping trips with us and my wife takes the bigger one in the gear well behind the seat of her Tarpon 120. Granted, these dogs are smaller than your Lab, but there is enough room for a cooler and the dog in the gear well.
The 140 model should have room for your Lab.
This comes up a lot
and there doesn’t seem to be perfect solution so far…
In the non tandem field
If you want to limit weight you have to go with something like a Hurricane Perception Phoenix 140 which is 52 lbs., because of the strutty thing forward of the seating area you might want to put the dog in the back well.
Or the Wilderness System Tarpon is similar at 62 lbs.
The 120 comes in Ultralight (retail 1450) 43 lbs.
Most SOT’s are 60 lbs+. If that’s not over your limit I would look in the kayak fishing forum for SOT’s for big guys.
Otherwise a open cockpit tandem
Canoes actually tend to be lighter than kayaks.
There is the sort of hybrid class, again plastic and heavy
Native Watercrafts’ 14.5 solor is 65 lbs. They do have cross struts that sort of limit dog area though