From IQ to pi/4 DQPSK
The OP stated he was interested in $\pi/4$-DQPSK (not QPSK), so phase synchronization is presumably not an issue for him.

As far as the actual implementation is concerned, you'll save yourself some time if you become familiar with the bottom of pages 29 (symbol mapping) and 37 (differential detection) in this student paper. Ignore all the old TI DSP-chip specific information and the information on pulse-shaping, which is already built into GNU Radio (if the OP is using that). There is also a reasonable description of a simple timing recovery algorithm. It is serviceable in some scenarios, but not others.