JMHO but this doesnt sound like A BROKER to me at all. This sounds more like a personal shopper.
Say I am a busy business woman and I need help shopping for ,say a birthday present for my mom. I know she likes rare old books that are out of print.
I hire the PS to find it for me for a fee so I can work and have family time.
I think you could be on to something here. Say I want a Saint Bernard but live in a small one bedroom apt. By interviewing the perspective owner and determining what his needs/wants are you can help guide them in the right direction.
I once took an online test to see what i liked and disliked in pets and what I was looking for in a dogs temperment, size, activity level etc.
then at the end..it told me what breeds that would best fit what my needs.
For example, When the show Fraiser was so popular everyone wanted a Jack Russel. And unfortunately many people got one. So many ended up in rescues and pounds because they didnt realize they were hunter, diggers and had high energy levels and required alot of activity! She could prevent this!!
I think you could be on to something here.
Once you found the right pup for the prospective owner you could put them in touch with each other. Let them make the deal happen.
You could then provide a courrier service/cab service to deliver the pup.
I could be wrong but I dont think the OP's intent was to be a broker at all.
I think she has a great love of dogs and is trying to find a creative way to create a business involving something she loves.