[douglas]

I don't know the exact equations for it, but you actually would observe a difference in the pulsar's frequency depending on your speed. Because you are moving away from it, each pulse would have a greater distance to travel to reach you, and so the observed period would increase by the time required for the light to cover the extra distance since the last pulse reached you. This increase in period is exactly linear with respect to your speed relative to the pulsar. The time dilation due to high speed movement is not linear, so it will generally not exactly cancel the doppler effect. There might be one particular speed where you would observe the same pulsar frequency as the stationary observer, but in most circumstances it would be different.