Buttons shaped like the actual objects they depict are known as ‘Goofies’ (especially in the USA), realistic or figural buttons. They existed, but not commonly, before the 1930s. Examples included flowers, stars, acorns and shells.
They were very fashionable for ladies for a few years from 1936. Sometime between 1940 and the mid 1950s they morphed into something for children’s clothes.
The influential designer, Elsa Schiaparelli (1890-1973), was largely responsible for the mania for realistic buttons. According to Wikipedia she “was also renowned for her unusual buttons, which could resemble candlesticks, playing card emblems, ships, crowns, mirrors, and crickets or silver tambourines and silk-covered carrots and cauliflowers. Many of these fastenings were designed by jean Clement, Roger Jean-Pierre and Jean Schlumberger.” She was influenced by the surrealist art movement. Her couture house lasted from 1927-1954.
Why do we love Scotty dogs so much?
An article from a pet website has some information: https://www.terrificpets.com/articles/10210965.asp
An British artist who moved to America, Marguerite Kirmse, was very successful drawing animals, dogs in particular, including Scotties, in the 1920s.
One early example in pop-culture were “Ric and Rac”, a Wire Fox terrier and his Scottish terrier buddy in the 1930s. They were carton characters created by Paul Abraham (professional name Pol Rab) that featured in a French newspaper. They were so popular that their images were used for brooches, housewares and ornaments. As scotch terrier/fox terrier style buttons date from the late 1930s, they may have been an inspiration.
The famous pet of Franklin Roosevelt, Fala (1940-1952), further cemented these iconic dogs into our consciousness.
Advertising from (?American) magazines show more scotties. They date from 1937-1940, and were shared on Pinterest.