Backstory: Recently I found someone to cat sit my cat for a week while on vacation. It took a few facebook posts in the right group to find someone. Once I met up with the cat sitter, she mentioned that most of her cat clients come from rover. I didn't realize rover had a cat section.
The Idea: A Cat Sitting App.
Deep Dive: Similar to Rover, you would build a two sided marketplace for cat sitters and cat owners to connect. Your marketing would be 100% catered to cats. Rover treats cats as an afterthought, and they should, it's a smaller, less lucrative market but you could still have a profitable business from just cats.
Validation: Rover proves that people will connect for both dog and cat sitting.
Monetization: You would take a fee from the cat sitting payments.
Steps to Launch: To help build up a list and gain some initial traction, you could start in your home town and create a simple landing page for local cat sitters. Join every local cat facebook page and every time someone posts about finding a cat sitter, you would share your page. This would be a good sample set of initial customers to poll for features and viability. Once you do launch, you'll have a group of initial users in one city to make the app not seem so empty.