If you’re going to set your prices based on what some random collection of uninterested bystanders thinks is “reasonable” – or if you set prices based on anyone else’s idea of what is reasonable, or indeed, if you let anyone else in the world set your prices – then you might as well snap the collar around your own neck and let them walk you, too. For a reasonable fee, of course.
Why set “reasonable” rates? If you expect to make a living at this, then what are your needs and how many hours can you walk in a day? Divide one by the other, add a little margin on top of that, and that is what you must charge. On the other hand, if all you want is some doggy companionship to accompany you on walks that you absolutely must take, then maybe you should pay the owners to rent their dog for awhile.
Somewhere between those two extremes you should be able to find a rate that enables you to walk the number of dogs that you’d like for the time that you’d like and to make an income that you can live with.