Can I do a 6-week online cooking course for a DTV visa and extend it for another month in Thailand?

Fake class. Online. Very strange. If you want it online just stay in your country.

Why would an online class qualify for the DTV? They issue the visa so you can attend in person

You do realise you can do online cooking classes from anywhere in the world?

You have to check with your embassy on how long the class must be in order for them to accept it for DTV. Every embassy has different rules and guidelines. Online classes generally do not qualify for a visa as the visa is issued for you attend a class in person in Thailand.

You won't be able to extend the DTV unless you're actively taking the class. But you can just leave and return and get a new 180 day stamp as many times as you want. There is no reason for anyone to extend a DTV when it's that simple to get a new stamp.