QPSK, from Square Root Raised Cosine to Rectangular Impulse Shaping
You can use rectangular pulses, but it is not necessary to do so.  Rectangular pulses have advantages and disadvantages.  The advantage is that they are very simple and easy to use, both for the modulator and the demodulator.  It makes life easier for the demodulator because it makes symbol timing very forgiving- you can be off on where you sample the symbol and still get a good measurement.

There are two disadvantages to using rectangular pulses.  The first is that it uses a lot of bandwidth.  The Fourier transform of a rectangular pulse is a sinc function, which drops off very slowly.  The second disadvantage is related to the first- very few real world solutions use rectangular pulses because they use a lot of bandwidth.  If you want something realistic, in terms of what most designers would do professionally, you should not use rectangular pulses.

You could, perhaps, get it working with rectangular pulses, and then when it is solid reintroduce the root raised cosine pulses.