You need to add the form tags and submit button to your form. In the form tag set your action to the page name of your whois page.
In your whois page you will need to add php code to POST the form data to the page. You will then use php to insert that data into the form field on the whois page.
If this all sounded like greek to you I suggest you go through a tutorial or two using forms in PHP. I found this one
http://www.tizag.com/phpT/forms.php but there are plenty. Its really pretty simple, but running through a couple of tutorials will help you integrate it into your site. You need to learn a little bit about forms and php to make this work.