Islam is not wholly confined to the Qur'an. Other major influences include:
The behaviors, sayings, etc., of the Prophet Muhammad, i.e., hadith.
This is the most influential source outside of the Qur'an, and there are commonly accepted sharia regulations which are not mentioned in the Qur'an (e.g., a women not praying when she has her menses).
The behaviors, sayings, etc., of the companions of the Prophet Muhammad, i.e., the sahabah.
History and culture during the advent of Islam.
How early scholars have made rulings.
Islamic laws (sharia) is generally derived from the Qur'an and ahadith, and we use other evidence to ensure it's been interpreted accurately. Consequently, it's misleading to say "sharia is not present in the Qur'an". E.g., the sharia prohibition on the consumption of alcohol (and other intoxicants) is in e.g. Qur'an 2:219.
Sharia ranges from the routine (e.g. pray 5 times per day) to dramatic (e.g., qisas). Most aspects of sharia can be considered routine; it's everyday things such as behaving appropriately when interacting with others. More dramatic aspects should go through a sharia court system.
(See also What is Sharia Law?)
Regarding Tawhidi: he's not an authority in Islam.
Imam Mohammad Tawhidi: The problem with the media's favourite Muslim writes:
In a letter, Al-Mustafa International University said:
"In spite of given warnings and notifications, the above-named person did not take heed of them each time and had not satisfactory academic record in his courses … he was placed on probation and [dropped] out on March 27, 2012 … the aforesaid person has no educational degree (or any given score) in his profile … Al-Mustafa University does not recommend Mohammad Touhidi for lecturing in any way. Accordingly, he has no competency to do religious activities or to preach sermons."
Welcome to the Weird World of Australia's 'Fake Sheikh', Mohammad Tawhidi writes:
Tawhidi is not recognised as an Imam or Sheikh by either the Australian National Imams Council or its South Australian equivalent, nor is he affiliated with any Australian mosque or prayer centre.