A "peg" is actually a measurement for alcohol. In 17th/18th centuries drinking vessels (tankards) made of wood had pegs at intervals, measuring about 60 ml (or 2 fl oz in those days). This would be for any spirit, especially gin in the early 18th century I suppose.
I came across this word reading stories of the British Raj, where people seemed to refer to pegs, or chota pegs (chota being Hindustani for small) quite often. Chota wrt drinks came to mean half measure.
Chota hazri was a pre-breakfast breakfast, also small!