Excellent shot! Now, regarding your question, if shooting birds is your main goal, or generally speaking shooting on the long side of lenses, I do not think switching to a D800 will make a lot of difference to the results, except for a little different shooting experience (heftier body, better viewfinder while shooting FX). In this case, I would probably wait for a D400, if the better handling (at least for me) and (maybe) higher pixel count are important to you.
On the other hand, if you also use a lot of wide / normal lenses, that's where FX shines. In this case I would switch to the D800, you don't loose anything on the DX-side (except for the DX-part of the viewfinder being smaller than the D7000 viewfinder), but you gain the FX advantages.