You've hit upon one of my pet peeves and one that I've emailed both Airbnb and VRBO about several times. It seems incomprehensible that you can search for a home in a windmill but not one with a fenced yard.
I travel extensively with my dogs for dog shows as well as vacations and I've spent hundreds of hours googling "Nova Scotia Airbnb fenced yard" (as an example) and I have found some wonderful properties (unfortunately, none in the part of the country you're searching) But it is extremely time-consuming. ( I found one incredible property in Nova Scotia that did not have a fenced yard but it was an island with a short causeway separating it from the mainland and I brought along two x-pens to act as a barrier to the road.
Hopefully, Airbnb will listen and add a filter for us dog lovers in the near future. Good luck with your hunt!