I have had chicks hatch from a mama hen & I have even had day old chicks from a hatchery, but I have never had quails. DO they need any different care then a baby chick. And gosh....they are small eggs, I bet they are gonna be super small!
First off, they need higher humidity during incubation and hatching. I try to keep mine at 50% for incubation and at least 70% for the hatch. Baby quail are small, and need their food ground up for the first week or so, depending on what kind they are. Coturnix would be okay after a week, buttons need it ground at least 2 weeks. They also seem to do better when the brooder is hot for the first few days, at least 98 degrees. But they don't need heat as long as chickens do, by 4 weeks they can go without. You will also need a smaller-based waterer, I use parakeet waterers for my babies. But you could get a quail water base also. I think that's it, if I think of anything else I'll repost
Usually I hatch quail slightly higher humidity but I had a 95% button quail hatch with 55% humidity cause I was incubating some chicken eggs with them and didn't want to raise it too high. Quail are pretty hardy and not too picky about hatching conditions.
They do usually need their starter ground up and preferably a higher protein starter than what you use for chickens. Gamebird feed or turkey starter works well. They drown very easy. I lost 2 coturnix to drowning despite putting things in the waterer and not filling it all the way. I finally filled it all the way with grit so they pecked between the very little rocks. Now that they are getting bigger they have knocked some of the grit out on their own so it gets slowly deeper.
We hatch quail every year, marbles in the waters work great, food has to be ground so they can eat it. They are about the size of a yellow jacket and they swarm if they chill and will smother each other so make sure they stay warm enough.