It is either "take-out" or "takeout." Take-away food is nothing new and goes back to the beginning of civilization, but the restaurant tradition appears to have spread widely in the 1930s.
(Oxford English Dictionary)
take-out, a. and n. Also take out, takeout.
Applied to prepared food sold for consumption elsewhere. Cf. TAKE-AWAY a. 1.
1968 Globe & Mail (Toronto) 17 Feb. 47/4 (Advt.), Soft ice cream and take out food. 1970 Times 29 Jan. 27/3 One of New York's finest restaurants will provide gourmet 'take-out' lunches for the hard-pressed executive.
take-away, n. and a.
1. That may be taken away; spec. designating cooked food sold to be eaten away from the premises of sale.
1964 Punch 15 Apr. 572/3 Posh Nosh..was serving take-away venisonburgers.
2. Of, pertaining to, or characterized by the selling of cooked food to be taken away.
1971 Guardian 18 June 11/5 Every take-away pieshop and baker sell a Cornish pasty. 1973 Times 3 Feb. 13/5 Leslie's also do a take-away service.
27 February 1932, Washington Post, pg. 2:
HING FAR LOW
729 1/2 11 St. S.E.
Chow Mein Specialty
Orders to Take Out
24 June 1939, New York Herald Tribune, Clementine Paddleford column, pg. 9, col. 7:
EDITOR'S NOTE - Anyhow, only in the last two years have we noted that the "take-out" Chinese kitchens (no restaurant in connection with the shops) are springing up in every possible spot. Surely Chinese dinners (Col. 8--ed.) at home must be a growing idea - we didn't call it new. And as Mrs. Kane agrees - "chow mein is swell for a simple supper." We have a list of these Chinese ready-prepared food shops if it interests you. In Yonkers, Jackson Heights, Flushing - all given in the shopping guide today.
July 1947, American Restaurant magazine, pg. 31:
That first year the Spiller's (Alpheus D. Spiller's of York Beach, Maine - ed.) sold only fried clams, fried potatoes and potato chips to take out. In 1939, they added hot dogs and hamburgers to
their list and business continued to flourish.
Pg. 32, col. 1, shows Spiller's signs for 1938 and 1939.
April 1941, Telephone Directory (Wilmington, DE), Classified pages.
Pg. 109, col. 1:
De Matteis John
Italian Food a Specialty
Submarine Sandwiches to Take Out
500 N Union...Wilmgtn-2-9241
Pg. 109, col. 3:
Patsy's Italian Sandwiches
Special Submarine Sandwiches - Take Out
903 W 4...Wilmgtn-2-9433