I'm looking for a story that was probably written somewhere from the 1940s to the 1960s.
"Turning Point", a short story by Poul Anderson; you can read it at The Drabblecast. The extracts below are from the original publication in If, May 1963, where it is illustrated on the cover (however, the little alien girl is described in the story as having "long blondish hair" and wearing a "white loincloth"):
The story has a memorable first line:
"Please, Mister, could I have a cracker for my oontatherium?"
I think I read it in an anthology, possibly in the 1970s.
Probably the Groff Conklin anthology Elsewhere and Elsewhen (abridged UK edition titled Science Fiction Elsewhere), or else the Poul Anderson collection Time and Stars.
A group of human explorers landed on a planet with primitive aliens, living in hunter-gatherer villages.
The indigenes were savages. That is, they depended on hunting, fishing and gathering for their whole food supply. So we assumed there were thousands of little cultures and picked the one that appeared most advanced: not that aerial observation indicated much difference.
Those people lived in neat, exquisitely decorated villages along the western seaboard of the largest continent, with woods and hill behind them.
The native people learned the human language before the explorers could learn theirs.
But from the first there were certain disturbing symptoms. Granted they had human-like throats and palates, we hadn't expected the autochthones to speak flawless English within a couple of weeks. Every one of them. Obviously they could have learned still faster if we'd taught them systematically.
Then the natives suddenly started producing technological innovations far beyond what they originally used. I remember that wooden sailing ships suddenly replaced their canoes.
"Pengwil . . . a Dannicarian name, all right," Baldinger muttered. "But they never heard of this island till I showed them our map. And they couldn't cross the ocean in those dugouts of theirs! It's against the prevailing winds, and square sails—"
"Oh, Pengwil's boat can sail right into the wind," Mierna laughed. "I saw him myself. He took everybody for rides, and now my father's making a boat like that too, only better."
Finally, the explorers realized that the natives were much, much smarter than us and that Earth faced a serious problem.
The hypothetical superbeings had always seemed comfortably far off. We hadn't encountered them, or they us. Therefore they couldn't live anywhere near. Therefore they probably never would interfere in the affairs of this remote galactic fringe where we dwell. But a planet only months distant from Earth; a species whose average member was a genius and whose geniuses were not understandable by us: bursting from their world, swarming through space, vigorous, eager, jumping in a decade to accomplishments that would take us a century—if we ever succeeded—how could they help but destroy our painfully built civilization?