Green’s Dictionary of Slang

whirl n.

1. [20C+] (US) a chance, an opportunity, a ‘go’.

2. [1910s] an outing (lit. or fig.).

In phrases

do one’s whirl (v.)

[late 19C] (US) to serve a sentence in prison.

give something a whirl (v.) (also give it a whirl, ...twirl, take a whirl)

[late 19C+] (orig. US) to try something out.