I am really not comfortable with this idea, at all. This sounds like organized "Dog flipping" to me, or worse, like Natasha said, an outlet for backyard breeders and puppy millers. How exactly is this supposed to work? Someone pays you (hundreds!) to post pictures of their dog on a website to they can rehome them? They send their dog to a foster home for that fee? Is this just meant to be home-to-home rescues? How would you screen people both re-homing and adopting the dogs if it's just online? How do the dogs get from home to home? Do they have to be neutered and vaccinated? Do the people rehoming the dog get paid anything? How are you going to prevent problems like people "rehoming" stolen dogs? Or worse, dog fighters looking for live bait? This really just sounds like a pet-exclusive Craig's list.
First of all, the fee of $5-1500 to pay someone to rehome a dog is ridiculous and outlandish. As someone who has worked in shelters I will tell you that the majority of people who rehome their dogs have to do it because they lack money--they've been evicted, they can't afford to care for the dog/dog's needs, and they can't find a rental they can afford that allows dogs/their type of dog. If people have essentially, a full month's rent to spare, they can probably find a new home for their dog alone, or not even need to rehome them.
There are already a lot of shelters that do "home to home" adoptions, listing pets for adoption on their pet adoption list but the animal is in their own home until the new one crops up. If you really want to help keep pets in people's homes, a business is just not really the way to go. It's got to be a charity, unless you're selling something that will somehow benefit those in need. It's kind of like trying to help the homeless by selling houses...to the homeless. The people who have the money to keep a business running don't need the service, and the people who WOULD use this service are likely people who are abusing and exploiting dogs for profit. I think your heart might be in the right place but you need to do a lot more research into the rescue world, and the extreme dangers of selling OR rescuing animals, purely online.
You need to either completely revamp or scrap this idea.