You're right, that feature is missing from the site, although there is an area under the Features & Facilities section where there is a ' Pets Allowed' check box.
I was wondering if it was worth adding a 'Pets Allowed' search option on a future update? I have personally never known anyone in Bangkok with cats and dogs, but there are probably more pet owners around than one might think. If they are indeed a rare breed, it would be an unnecessary feature to add if there were only say 3 people using it a year.
Any feedback from the forum on whether such a feature would be useful or not would be appreciated. Don't forget though, you can overdo a search function. Just imagine, if there were too many options, we'd all be searching for the perfect home in the perfect location at the perfect price, with bags of space, free WIFI, Cable TV, and a maid to boot, and the result of such heavenly accommodation would invariably result in 'No Results Found' every time.