Do all proteins have quandary structure?

No.

Proteins start out as a Primary structure, which is just the linear form and sequence of amino acids.

The proteins then start forming alpha helices and/or Beta sheets depending on the properties of the amino acids. This is their Secondary structure

The proteins then fold completely into tertiary structure. Here, we have a lot of hydrogen bonding and hydrophobic interactions within the protein between the helices and beta sheets. Many proteins are fully functional in their tertiary structure and don't have any reason for forming into a quaternary structure.

In the quaternary structure, we usually see an interaction between 2 or more polypeptides or proteins. An example would be 2 proteins in their tertiary structure binding together to become a functional dimer. If 3 proteins were interacting it would form a trimer.

Several proteins are functional only in a quaternary structure while several more proteins are just fine in their tertiary structure and therefore do not have a quaternary structure.