Digital Performer has an excellent doppler effect, but it would be rather expensive to buy DP just for that.
I have also created the doppler effect with the Serato Pitch'N'Time plug-in, which is even more expensive than DP.
The doppler effect itself is the sound being "compressed" and then "stretched" by the motion of the sound source - a truck horn or a jet, for example. As the sound approaches you the sound waves are compressed as they approach the listener; the compression of the sound waves raises the pitch of the sound. When the sound is next to you it is back at the original pitch, then is "stretched" as it recedes from the listener, lowering the pitch.
I don't know what DAW you are using, but there are a number of free and shareware plug-ins out there, but I've never used any of them so cannot comment on the quality or accuracy.
Just for fun, the Leslie speaker (which is usually used on the Hammond organ) is based upon the principle of the doppler effect.