Most of us have that problem, even worse my Dawg pee's on my leg when I miss!

Size eight should be sufficient, just make sure they are in range when you shoot. (My experience is with Bobwhite quail---hope it helps.)

If you are hitting them but they are not falling, it is either too small a shot size or too long a range for your choke. I know that I am an exception here but I use #4 shot for quail and try to shoot at them when they are between 30-40 yards but I can deck them at 50 yards. One pellet drops them and passes completely through. If you are in brush and visibility is limited to less than 30 yards, you should be using smaller shot like #6 or #7. Quail can absorb this small shot and keep flying from 30 yards and further. Check your choke too. If you have an improved cylinder, it will really spread the shot pattern and limit your range. A modified choke is best for quail unless you will be closer than 20 yards.

Go with a 12 or 20 gauge and use 7 1/2s or 8s with a modified or improved cylinder choke.

If you are hitting them and they are flying away the two biggest problems you probably have are either having the wrong choke in or having bad shells. Make sure you don't cheat on shell prices, don't buy cheap shells that are low brass for hunting. Also you want a relatively tight choke. Another thing you can consider is changing the shot size to something a little larger.

Almost certainly, you are flinching. Geta 20 gauge and get some help at the trap range. People will volunteer.