what can i claim as a small business expense?

First, let me state you should be asking this question of your tax advisor as to what is deductible and what is not; it can be tricky. In order for items to be deducted they must be items that can only be used for your Rover business, so the vacuum is probably a big fat no as you can clean floors when you don't have clients. Cleaning supplies, bowls, leashes, poop bags, etc, probably yes

If you drive a lot to clients homes you can deduct your mileage; this is the largest deductible you can safely deduct. However, you need an IRS compliant mileage log. There are many Apps out there that can help you track your mileage. Also if you drive a lot you are using your cell phone for Rover cards, texts, and communicating with your clients; a percentage maybe up to 1/2 of your monthly bill may be deductible. These two items will eclipse the items you mentioned in your question.

Please seek out professional assistance at least for your first year - and best of luck