"Domain" is not a property of an LDAP object. It is more like the name of the database the object is stored in.
So you have to connect to the right database (in LDAP terms: "bind to the domain/directory server") in order to perform a search in that database.
Once you bound successfully, your query in it's current shape is all you need.
BTW: Choosing "ObjectCategory=Person"
over "ObjectClass=user"
was a good decision. In AD, the former is an "indexed property" with excellent performance, the latter is not indexed and a tad slower.