Yes, there are plenty of properties which allow you to bring your pet along on your travels.
In order to find out which ones do, go to the filter menu and select the "Pets allowed" option. You'll find it under the "Welcome" section of the menu.
After making your selection, click "Show listings", and you will see all the listings which allow pets in the property.
Be sure to contact the host and give details regarding your pet. Make sure they are fully aware and comfortable with your pet staying, before processing the payment.