Green’s Dictionary of Slang

1. to go around with women.

c.1800		‘Song No. 12’ Papers of Francis Place (1819) n.p.: Young men take warning, night and morning, / Just like me you go a Molling / You the same sad fate may share.
1864, 1867, 1870		Hotten Sl. Dict. 180: MOLL’D, followed, or accompanied by a woman.

2. of a man, to act effeminately.

1972

B. Rodgers Queens’ Vernacular 137: moll [...] 2. to walk, skip or mince.

3. (US) to work as a prostitute.

1954

Time 28 June 57: When a girl cannot get modeling dates in New York, there is nothing for her to do, it would appear, but to accept the $100 kind. She winds up molling for mobsters [HDAS].