No hadith, no qiyas, no istislah, no ijma, just Quran.
In fact, you can't take Hadeeth out of this equation.
No seriously, the Qur'an itself orders to always take Hadeeth in consideration:
4:59 يَـٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوٓا۟ أَطِيعُوا۟ ٱللَّهَ وَأَطِيعُوا۟ ٱلرَّسُولَ وَأُو۟لِى ٱلْأَمْرِ مِنكُمْ ۖ فَإِن تَنَـٰزَعْتُمْ فِى شَىْءٍ فَرُدُّوهُ إِلَى ٱللَّهِ وَٱلرَّسُولِ إِن كُنتُمْ تُؤْمِنُونَ بِٱللَّهِ وَٱلْيَوْمِ ٱلْـَٔاخِرِ ۚ ذَٰلِكَ خَيْرٌ وَأَحْسَنُ تَأْوِيلًا
O you who have believed, obey Allah and obey the Messenger and those in authority among you. And if you disagree over anything, refer it to Allah and the Messenger, if you should believe in Allah and the Last Day. That is the best [way] and best in result.
For the question, Allah prescribed laws for His Prophets to judge their people with, i.e. the Shari'a is a must for a proper Muslim society:
( 5/44 ) Indeed, We sent down the Torah, in which was guidance and light. The prophets who submitted [to Allah] judged by it for the Jews, as did the rabbis and scholars by that with which they were entrusted of the Scripture of Allah, and they were witnesses thereto. So do not fear the people but fear Me, and do not exchange My verses for a small price. And whoever does not judge by what Allah has revealed - then it is those who are the disbelievers.
( 5/45 ) And We ordained for them therein a life for a life, an eye for an eye, a nose for a nose, an ear for an ear, a tooth for a tooth, and for wounds is legal retribution. But whoever gives [up his right as] charity, it is an expiation for him. And whoever does not judge by what Allah has revealed - then it is those who are the wrongdoers.
( 5/46 ) And We sent, following in their footsteps, Jesus, the son of Mary, confirming that which came before him in the Torah; and We gave him the Gospel, in which was guidance and light and confirming that which preceded it of the Torah as guidance and instruction for the righteous.
( 5/47 ) And let the People of the Gospel judge by what Allah has revealed therein. And whoever does not judge by what Allah has revealed - then it is those who are the defiantly disobedient.