Probably I mis-explained my intention.
A firefox search plugin it's only a 'shortcut' for the search box in a website. It's only some tens of rows of code and I'm obiously able to do do it myself, but It need to be hosted on jquery.com, so a user, when come into api doc, can click on searchbox on FF and add the ability to search on api.
User enter a search term, click the search icon, then firefox simulate user has compiled the searchbox on jquery. and "submit the search form", like you were on website.
So search work is done from jquery.com website.