You could simply add a question form to your site, where Your user enters a question. By hitting the send button it redirects to q&a site.
There was a question about a question form at sidebar or on the frontpage. There is explained how to build a questionform.
You can see an example on my site: www.puerto-vallarta-directory.com , there is on mid of page a question form. If You enter a question You will be redirected to my Q&A site.
If this is what You are looking for, than it is not very complicated.
See here: http://www.question2answer.org/qa/549/how-to-add-ask-question-text-box-and-continue-button-sidebar
and see here: http://www.question2answer.org/qa/1635/how-to-have-the-question-form-on-front-page
The big advantage of q2a in this case is, that the question form consists of two parts. The first is a short question in one sentence from where You are directed to the larger form where You can add details, email, categories and tags. This second form is allready on the q&a site and besides the one sentence question no information runs through the web.
I dont know, but I think the method above shouldn´t have huge disadvantages, Just try it.