Hi - I'm in NZ and hatched out a couple of baby quails. I fed them Sharpes Meat Bird Crumble which is 19% protein and my birds grew up fine.
Mine were hatched by a broody quail hen, which is unusual, and this meant they were out in the pen with a dirt floor from day one and they were very quick to scratch around for bugs, so they had a bit of supplementation (but the pen is only about 1m2 and under cover so it's not exactly crawling with bug life). I started tossing them a scoop of compost from my garden every couple of days filled with bugs which they loved.
They are now fully grown and are much better at foraging than the older girls. One of them jumps up and nips my fingers when I reach in the cage because she thinks I'm bringing bugs to eat!
I now feed them dried mealworms which they absolutely love so I think you could supplement the food with those if you don't have access to live bugs. Otherwise the meatbird crumble is probably sufficient (even if people recommend 20%+) but they might be slightly slower to start laying. Mine turned out fine