Doppler shift is based on speed, the result of red shift is that stuff which is moving away fast enough to produce red shift is far away by virtue of being fast and stuff and stuff that is blue shifted needs to be far away or it will collide with you very quickly or just pass you by. The relative speeds required for doppler shift are pretty high speeds so you normally observe it in stuff that’s far away, but distance isn’t really a requirement for doppler shift to happen or be observed.