Chuck Strong on Invasion is from 1982 according to the label. I don't know which one was recorded first, but I would lean towards Gwen McCrae.
Don't think the Gwen McCrae version got a US single release: it's on the "On My Way" album, with "Keep The Fires Burning." Gwen's version was released on both 7 and 12" in the UK on the back of that track's success; both DI and KTFB were really big records in both the mainstream and underground clubs of the day.
Chuck Strong's version didn't come to the UK via the major importers, so didn't get the same exposure. I'm sure if it did it would have been massive.
Each version of "Doin' It" is terrific in their own right. Both still sound really fresh, giving lie to the theory that much 1980s soul sounds hideously dated. These are both fantastically cleanly produced soul records, played by great musicians and sung by great soul singers.