That's pretty difficult and not something you can really do with Q2A. You'd be better off using a vanilla script (could be PHP, could be Java or something else) to read the questions from the database and posting that information to the second site.
Assuming you don't have access to the database on the second site you'd need to implement a site scraper, grab the content and insert into Q2A's database. I've never done that with PHP but Jsoup is excellent and easy to use if you know Java.