First, it's spelled Quail. Fine little gamebird, with 4 or 5 species in North America.
410s, in non expert hands, will kill quail, but some of them may take days to die. Use an adequate gauge,anything from 28 to 12 can be suitable. 410s are not analogous to ultra light fishing tackle, an inadequate shot load or poorly placed shot is not sporting, it is callous and cruel.
Many hardcore quail fanatics use smaller gauge doubles of either variety. Common factors include fast handling, open chokes, and light weight.
Size 8 shot is usually the best choice.
I've shot more quail with 12 gauge pumps, but that's because I like pumps.
Whatever you decide on for a shotgun, do hit the range and get in some practice.
Finally,quail flush in coveys nigh simultaneously. Focus on ONE bird and take it. Later, you can try doubles, but in quail hunting a double is two singles taken back to back.
In 50 years of quail chasing, I've taken ONE triple. Quite proud of it,too.