Nope, you did pretty well with that one, especially since it was your first bird shot. Downy Woodpeckers are kind of tough to catch because they are so twitchy and you did well to catch one still like that.
Shutter speed, aperture, and ISO are always a balancing act and sometimes we have to settle for what we can get. When shooting birds shutter speed is very important. In my opinion more important than ISO or aperture. I like to keep my shutter speed between 1/1000 and 1/2000 but that isn't always possible (I shot some Wild Turkeys this morning at 1/20 second). When I can't get the shutter speed I want I open the aperture wide open and sacrifice depth of field, and then start raising the ISO some. Faster than 1/2000 is overkill much of the time so when I start getting that fast I start trading shutter speed for aperture or ISO.
For birds in flight I actually prefer a slightly slower shutter speed, somewhere around 1/500 second, since it allows the wingtips to blur some.