How do i determine if domains can be found using Javascript or JQuery?

jQuery/js are only able to send HTTP demands. You will need to make use of a whois service accessible via http. i.e. a script running in your server, or perhaps an API supplied by another person.

See Who provides a WHOIS API?

You cannot dependably get it done around the client side only, but when JS is the only option, you should utilize a 3rd party through either an API (for example http://www.whoisxmlapi.com/domain-availability.php) or low volumes of searches, you can easily parse it from another site (e.g. http://whois.domaintools.com/whatever.com)

You will find more integrated and far cleaner server side solutions if that is a choice - phpwhois for instance is thorough and free.