Singapore was a commercial and naval port in what was then British Malaya and the Straits Settlements.
At the beginning of Missee Lee the harbourmaster thinks they should "make straight for Singapore" rather than calling at China. (ML1)
When discussing their return home, Captain Flint says they will go to Hong Kong or Singapore, then promises Missee Lee to "touch nowhere before Singapore". Susan asks "How long will it take us to get to Singapore" (ML23).
At the end Captain Flint marks the position of the Three Islands on an 1879 chart which had Singapore in the left-hand bottom corner. On the Shining Moon they then "found their way to Singapore" (ML27)