Some owners are happy to take on a sitter who is travelling with their own pet - but as with all sits, it's up to the owner to decide exactly what they are looking for in a sitter.
If you would like to take your own pets with you, tell any owners you apply to about this in your initial message to them so they can let you know right away if it's something they would consider.
Or, you could consider buying a membership that lets you both apply for sits and find a caring sitter of your own. That way, you and your pets can enjoy the best of both worlds! You'll see an option at the checkout to select both sides when you buy your TrustedHousesitters membership, or go to the Membership section in your Settings area when logged in as a member.