Green’s Dictionary of Slang

(usu. nursery) sleep personified; thus soothing phr. the dustman’s coming.

1821		Egan Life in London (1869) 211: The Corinthian observed to his Coz, that, as the ‘Dustman’ was fast getting hold of Logic, they would be off without him.
1835		G. Kent Modern Flash Dict.
1848		Flash Dict. in Sinks of London Laid Open.