Great question, @melissa1984!
I had sworn there was a similar question asked a while back, but I cannot find it anywhere so it may have come from a different site- but in regards to pets and circles, one solution is to leave a special “gateway” for them when you draw the circle.
It can be as elaborate as drawing a special sigil or symbol somewhere in the border allowing for seamless travel back and forth for the specified entity (in this case, your cat), or as simple as saying: "I allow my cat to pass through this border at will. Doing so shall not break the sacred circle."
Feel free to do your spell and ritual work without worry. You can then take down the circle as usual when you are finished 
Good luck and blessed be! 