The 1919 square cent isn't particularly rare; it's the first year of issue of the type. I'd grade yours Fine to Very Fine, CV less than $1.
Actually, the Straits Settlements were originally part of India. In the early 1800's coinage for the Straits in the name of the East India Company was struck, with designs more or less the same as the ones used by the Company in India, only denominated in cents, not annas. Here's a (slightly warped) Company cent, 1845:

When the Company was shut down in 1858, the Straits became part of the new Viceroyalty of India. During this time, coinage for the area was made in the name of "India-Straits", still denominated in cents. It became a separate colony of Britain in 1867, with the name "Straits Settlements". My only example of "India-Straits" coinage is this sorry specimen, a rather corroded
Half Cent of 1862.

Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis