If I understand it correctly, the Buddy Rider dog seat is cantilevered forward of the seatpost and tends to bend the seatpost towards the handlebar. The main load on the seatpost is from the rider themselves, cantilevered backwards from the seat tube clamp and bending the seatpost away from the handlebar.
The Buddy Rider dog seat would actually reduce the bending moment at the base of the seat post. If the total weight of you, your dog and the dog's seat is below 110kg, you are probably good to go exactly as is.