Doppler Effect in Slow Light

The definition of slow light in the link

Slow light is a dramatic reduction in the group velocity of light, not the phase velocity. Slow light effects are not due to abnormally large refractive indices, as will be explained below.

To clarify,here is an animation with different phase and group velocities,

This shows a wave with the group velocity and phase velocity going in different directions. The group velocity is positive (i.e., the envelope of the wave moves rightward), while the phase velocity is negative (i.e., the peaks and troughs move leftward).

The Doppler shift

is the change in frequency of a wave in relation to an observer who is moving relative to the wave source.

affects the frequency of a wave, but the slowing of light is in the group velocity, the Doppler shift would be the same as if there is no group velocity just light moving at c at the basic frequency.