Which Prime lens for Bird Photography?

Yes it will be fine on a D7000. VR is overated, if you have sufficient shutter speed you won't need it anyway. The D7000 is reasonably good on high(er) ISO to get you to those higher speeds....
As someone says above get the Teleconverters. A 1.4 and 2x TC will make it a 420 f4 and 600 f5.6 respectively.... All 300 2.8's weigh a proverbial tonne....just somethng to be aware of.....
As someone says above get the Teleconverters. A 1.4 and 2x TC will make it a 420 f4 and 600 f5.6 respectively.... All 300 2.8's weigh a proverbial tonne....just somethng to be aware of.....

If the 300 is an AF-1 version rather than a later AF-S version - use caution.
The AF-1 was last made 16 years ago and many spare parts, especially the AF motor, are no longer available. It was a good lens - but generally cannot be repaired. Allow for this in the price you pay
Turning to VR, VR lenses are probably outside the OP's price range, but I own and use a 300 f2.8 VR and disagree all the VR feedback.
Nikon make the point VR helps steady the subject in the frame, helping get good AF lock on. I agree VR does not help reduce subject movement much faster than 1/500 shutter speed - but this is an academic arguement if AF misses a moving subject because VR was not being used.
The 300 f2.8 VR has tripod mode VR
Tripod mode VR can help a lot at slower shutter speeds, and with a converter - 560-840mm equivalent angle of view on a D7000. VR can sometimes make the difference between sharp and unsharp; or head and wing feathers within the depth of field - this may need f11 or smaller - with a tight crop of a medium or small bird.
The AF-1 was last made 16 years ago and many spare parts, especially the AF motor, are no longer available. It was a good lens - but generally cannot be repaired. Allow for this in the price you pay
Turning to VR, VR lenses are probably outside the OP's price range, but I own and use a 300 f2.8 VR and disagree all the VR feedback.
Nikon make the point VR helps steady the subject in the frame, helping get good AF lock on. I agree VR does not help reduce subject movement much faster than 1/500 shutter speed - but this is an academic arguement if AF misses a moving subject because VR was not being used.
The 300 f2.8 VR has tripod mode VR

Tripod mode VR can help a lot at slower shutter speeds, and with a converter - 560-840mm equivalent angle of view on a D7000. VR can sometimes make the difference between sharp and unsharp; or head and wing feathers within the depth of field - this may need f11 or smaller - with a tight crop of a medium or small bird.