The Carr Fastener Company was apparently related to the F. S. Carr Company of Massachusetts that existed in 1895 (if not before), named after Fred Spafford Carr (1874-1967). They opened an England branch in Stapleford in 1911, and a Canadian factory in 1920. In 1928 a merger saw the company renamed the United-Carr Fastener Company.
They have been located in South Australia since 1928, where they are still operating. Carr-Dot fasteners are now made by Mitchell & Cheesman, South Australian manufacturers since 1957.
In the past they supplied buttons, snap fasteners and other items for the Department of Defence.
They made fasteners for motor cars, as well as for clothing. Here is a (slightly blurry) picture from Museum Victoria’s collection of a sample card of fasteners c.1950:
Museum Victoria https://trove.nla.gov.au/work/230626894?sortby=dateAsc&q=%22Carr+Fastener+Co%22&c=picture&versionId=254111476
For more on snap fasteners; see https://www.thefedoralounge.com/threads/dating-clothes-by-snaps.75667/
Detail from 1958 Tariff Report
These were made under license in Australia by the Carr Fastner Co.
“Put away your needle and thread! Do without buttons and button-holes! These STRONGER, SIMPLER, FASTENERS are QUICK to put on, SPEEDY in action & LAST A LIFE-TIME OF LAUNDERING … DAD likes them … MOTHER needs them ... JUNIOR loves them … EVERYBODY wants them…”
These cousins (and superior competitors if you are to believe the advertising) of buttons were marketed in the Australia Women’s Weekly from 1950 to 1960.