nog n.

1620s, "small cup, mug," later of the contents of such a vessel, "small drink" (1690s), a word of unknown origin, possibly related to Norfolk dialectal nog "strong ale." OED considers that the similar Celtic words are "no doubt" from English. Informal meaning "head" is attested by 1866 in American English.

also eggnog, "sweet, rich, and stimulating cold drink made of eggs, milk, sugar, and spirits," c. 1775, American English, from egg (n.) + nog "strong ale." Old recipes for the drink could be made with weak alcoholic beverages like beer or wine in lieu of the milk.

… And Bryan O'Bluster made love to egg nog, 

And pester’d the ladies to taste of his grog; 

Without it (said Bryan) I never can dine, 

’Tis better by far than your balderdash wine,

It braces the nerves and it strengthens the brain,

A world and no grog is a prison of pain,

And MAN the most wretched of all that are found 

To creep in the dust, or to move on the ground!

It is, of all physic, the best I have seen 

To keep out the cold, and to cut up the spleen —

Here madam — miss Cynthia — ’tis good — you’ll confess — 

Now taste — and you’ll wish you had been in my mess.

[Philip Freneau, The Passage to Burlington, ca. 1790]