Hobson Jobson (1903) the great dictionary of Indian words in English, defines "Dhoby, Dobie s. A washerman; H. dhobi [from dhona, Skt. [Sanskrit] dhav, 'to wash.'] In colloquial Anglo-Indian use all over India. A common H. [Hindustani] proverb runs: Dhobi ka kutta ka sa, na ghar na ghat ku, i.e. "like a Dhoby's dog belonging neither to the house nor to the river side." [Dhoby's itch is a troublesome cutaneous disease supposed to be communicated by clothes from the wash, and Dhoby's earth is a whitish-grey sandy efflorescence, found in many places, from which by boiling and the addition of quicklime an alkali of considerable strength is obtained" (Hobson-Jobson, 1903, p. 312).
Johnston & Hoffman, possibly the publisher of this postcard, also offered the same view in black & white.