No, don't use threads for that.

You should restructure your program in a way that it first issues all DNS requests for all domains and after that checks the DNS responses it receives from the resolver. This could be done with the ->bgsend method if you want to keep on using Net::DNS::Resolver. If you want to use AnyEvent::DNS, a combination of $cv->begin and that module should also enable you to fire off the DNS requests in one go.