At least from this brief entry, your English appears to be more than elementary.  I was going to do a correction, but it actually looks pretty good to me.  My only suggestion would be to look at the word "seriously."  If you are "seriously looking," that simply means you are devoting a lot of time to looking.  

However, I wonder if you don't mean まじめに探している...

If so, I think that a better way to say it would be:

"I'm looking for someone who wants to do a serious Japanese-English language exchange with me."

or

"I'm looking for a serious Japanese-English language partner."