How do I get a different picture in the profile space? The ones they offer are fine but I would really like a K-wing in there.

You can get whatever profile avatars they are offering. But be advised FFG rotates out profile pics.

So I am just going to have to wait until some ships come around?

They got rid of the X-Wing avatars last year. I don't know that they had a K-Wing in the mix before the change. We don't know if the X-Wing avatars are ever coming back. Those of us who had X-Wing avatars got to keep them for some reason.