The earliest match for "Act your age, not your shoe size" that a Google Books search finds is one from 1967 cited in Charles Doyle, Wolfgang Mieder & Fred Shapiro, The [Yale] Dictionary of Modern Proverbs (2006):
Act your age, not your shoe size.
1967 Barbara Schoen, A Place and a Time (New York: Thomas Y. Crowell) 57: "'Why don't you act your age, not your shoe size?' said Paul. He made a disgusting face and ran out and slammed the door." 1981 Pittsburgh Post-Gazette 5 Feb.: "The high school students put their feelings succinctly, when they made signs which urged the negotiators to 'act your age, not your shoe size.'" The proverb originated as an anti-proverb based on "Act your age."
Google Books confirms the Schoen citation as being from a novel published in 1967.
A related anti-proverb listed in the same dictionary is "Act your age, not your IQ," for which the dictionary gives a first citation date of 1995. A Google Books search, however, finds an instance of this expression in Student Lawyer, volume 16 (1987) [combined snippets]:
BIG APPLE TO BOY: ACT YOUR AGE, NOT YOUR IQ
The New York Court of Appeals ruled that Steve Baccus could not sit for the state's bar exam last February because he was four years shy of the 21-year-old age limit. At 17, Baccus, who attended the University of Miami School of Law and passed Florida's bar exam after receiving an age waiver, is dubbed the youngest lawyer in the United States.
Another early instance of "Act your age, not your IQ" appears in Jolene Prewit-Parker, Homecoming (1990).
A Google Books search also turns up multiple instances of "Act your age [and] not your color," dating back to Clara McLaughlin, The Black Parents' Handbook: A Guide to Healthy Pregnancy, Birth, and Child Care (1976) [combined snippets]:
If you make negative statements to your child about him or black people in general, the child will associate blackness with inferiority. How often have you heard the statement "Act your age and not your color"? What does this tell your child?
All of these expressions appear to be extended variants of "Act your age," which Jonathon Green, Cassell's Dictionary of Slang (2005) identifies as originating in the United States:
act your age! excl. (also be your age!) 1920s+) (orig. US) a term of contempt, based on condemning someone who the speaker considers is acting childishly; also ext. as act your age, not your shoe size!
The earliest search result matches that I've been able to find for "Act your age" are from Life magazine, volume 85 (1925) [text not shown in snippet window]:
"Act your age, kid, act your age," was the prompter's admonition.
and from the [Brownwood, Texas] Yellow Jacket (October 13, 1926):
Fella: I have been searching for you through countless aeons. I feel that we must have known each other since the beginning of time.
Girl: Act your age.
Both of these instances are indeed from the United States.