'Date', as in "She's my date for tonight" first appeared in the USA in the 1920s in a publication examining Ameerican speech. 'Dating', to mean the process of meeting/going out with one's 'date' did not appear until the late 1930s.
I assumed in my earlier response that you did not mean the process of 'dating' such as is used by archaeologists to place an item in its historical context!
It's one of the features of English that nouns, like "a date", can readily be turned into verbs, like "dating" -- or the other way round.
People complain about it, but Shakespeare did it a lot...
When it really rankles is when there's a perfectly good verb already. Why use burglarise instead of burgle, or leveraging instead of levering?