1941 Irish Times 24 Nov. 5/7 The Goodwill Restaurant is serving 6,000 midday meals a week, 1,000 take-aways.
And for the verb it has this:
1894 Daily World (Lawrence, Kansas) 13 Sept. The same persons who came when it was first opened are still among the number to be seen there, either procuring food to take away or getting it at the long counters to eat at the room.
And the North American take out is a bit older:
1940 Mason City (Iowa) Globe-Gaz. 29 Mar. 11/1 Our day and night fountain service is finding favor with late folks. Counter served or take-outs.
And the verb:
1919 Jrnl. Industr. Hygiene Sept. 239/1 There was a cafeteria not far from the works, where they could go for lunch or could get food to take out.
I’ll say again, the Online Etymology Dictionary isn’t the greatest resource. It’s mainly cribbed from the OED, and often from older entries at that. In this case, the OED updated these entries in September 2015. It’s not bad as a free resource for a quick check of something, but it’s far from the final word.