I would get the train from Waterloo to Hersham and visit Surrey Pet Supplies - have a look at their website for opening hours and directions etc. Its about 30 minutes by train. There is a large warehouse selling goods and upstairs are so animal displays, certainly worth the trip. Not a lot else at Hersham though.
TFL website will give details of travel in/around London and then you can Google Maps the places suggested.
Travel is dear in London so a taxi will most likely be out of the question, but you can get one day travel cards etc.
I guess you won't have much spare time.