To propose Qur'an as the sole constitution is easier said than done, given the present state of affairs. Even in Qur'an only groups there are major divisions! If Hypothetically Qur'an was made the constitution of Pakistan (which is an tough given the nature of belief of the masses) then the question will be raised over it's interpretation. There will be a big chunk of people who will fight for the Qur'an to be implemented by the so-called Prophet's Sunnah (logic being, he is the sole representative to show Qur'an true interpretation/implementation). Even if a Qur'an based constitution were adopted (no sectarian interference allowed) then how will the state treat those who will put up a fight and big resistance? Declare them rebels/misguided/heretics and then declare a war against them? How will that play out in terms of UN charter on human rights?
Some things need to be thought thrrough keeping the realities of the ground in mind.
Keeping in view of the above, some perhapss will propose "Religious Secularism" whereby a Parliament declares it will not legislate any law against the Qur'an and then people are left alone Islam according to their understandings/sect. That will leave wide open room for rebellion because some will declare the government unIslamic (because it is based on Qur'an alone) and declare a Jihad against it in the name of Qur'an and Sunnah if not against Shariah or Shahadat. We see that is being done in parts of Pakistan already.
Europe went through hundreds of years of religio-political wars over a similar issues and at the end decided it was best to separate religion from politics. Since then they have enjoyed relative peace and abhor the idea of ever allowing a Papal rule/protestan opposition to be brought back.
So, what then is the solution? Time for brain storming.
Here is a discussion somewhat related to the subject which may help us along the way: