my instructor had allready pushed down hard on the yoke
Bad plan. Birds will usually dive out of the way - I see this on pretty much every flight I do. Trying to outdive or outfly them is simply stupid - they are much better at it than any of us here ever will be! Of course I wasn't there, but I'm reasonably certain that had you just motored on, nothing would have happened.
As for the landing - yes, would have done the same, especially in your situation with an airfield readily available.