Please make it clear before booking whether you are genuinely dog friendly or just dog tolerant. The worst thing is when you book somewhere that claims to be dog friendly but when you arrive you get presented with a list of rules that make it clear that the owners want your money, but really didn’t want the dog. If you don’t want dogs upstairs or on furniture (or in one case, on the rugs, no problem, my dog knows how to levitate!), make it clear in advance.
In a properly dog friendly Airbnb, I’d want to see lots of fleece throws for the furniture (more than one per sofa, so that they can be changed over the week). A stack of old towels for muddy paws (just one would be soggy in no time in the winter and that would end up smelling nasty). A couple of bowls because if someone forgets theirs, they would probably just grab some from the kitchen cupboards which is a bit grim. A roll of poo bags (if only as a hint that you expect people to not leave dog poo in the garden). A warm outdoor dog wash area would be absolutely amazing and my dog would love you for it. Plenty of rugs - hard flooring can be slippy and carpet can hold on to smells, rugs can be taken out to air or just replaced much more easily. No reed diffusers or plug in air freshener things, many are toxic to dogs, and they just layer smell on top (I’d be wondering what you were hiding). And a small securely fenced area just outside the back door, with a light and maybe a bench, would be essential. A washing machine and dryer would be a huge plus, as would a decent hoover.
Personally, I try to avoid properties that are merely dog tolerant. They feel much less welcoming and relaxing. If the bare minimum is provided in terms of throws and towels etc, there’s more likely to be a lingering doggy smell, so it’s really the worst of both worlds.
I think whether allowing dogs will lead to more bookings will be largely dependent on location. If you’re somewhere with good walks and dog friendly local businesses, it will be well worth it. Most people holidaying in the uk want o take their dogs with them. If you’re in the middle of a big city though, you’ll probably do better by guaranteeing dog free accommodation.