Multi level search box

Hi, i need some help figuring this out. I want to create a search box that enables me to search a category, then the next field the child category, so for example, on my homepage search I want to be able to search for dogs (category) then next field a dropdown of all the dog breeds (child category) then location and hit search. not sure what this sort of search box is called sorry but it’s similar thing as car make and model search.

Thanks in advance

The blog I need help with is: thepet4you.co.uk

The page I need help with: [log in to see the link]