I'm assuming these were hand held then. The general rule of thumb for hand holding a shot is that the shutter speed should be the reciprocal of the focal length. But this only works with 35mm equivalent.
If you were at 300mm, with a 1.6 teleconverter, shooting with an XSi, you have a 35mm equivalent focal length of 768mm. This means your shutter speed should be at least 1/1000 of a second if you want to have a chance at a sharp capture. I don't remember offhand what the aperture of that lens is at 300mm, but I'm guessing with the TC on there, it was pretty dark. To keep your shutter speed up, you would need to bump up the ISO, which would introduce noise, but would likely allow you to get a sharper picture.
There's also the chance that you did all this anyway. EXIF would be useful in this case, but I suspect that your shutter was too slow. My main evidence of this is your last shot of the buck running away. There's considerable motion blur in the background and on the buck. If you were shooting at 1/1000 I think there would be considerably less blur.