Quiz Kids began on radio in the early 40's, and transitioned to television in 1949, first airing on NBC before moving to CBS. The first TV run ended in 1953, only to be revived for a few months in 1956. It aired in primetime, as a lot of quiz shows did back in those days, presumably early in the evening so kids could watch their peers before retiring for the night.
The series has been revived here a few times and in Australia over the years, but not in the last 20-odd years. The last version, under the title Quiz Kids Challenge, was hosted by actor Jonathan Prince (ex-Throb) in 1991, and lasted one season. Before that, veteran game show host Jim McKrell (ex-Celebrity Sweepstakes) fronted the first revival in 1978. Three years later, sitcom legend Norman Lear stepped from behind the camera to host a short-flight version for CBS.
The original series, of course, was well before my time, so there won't be a rating. We'll leave you with a 1951 episode, presumably airing on CBS, with guest host Fran Allison (Kukla, Fran, & Ollie):