Yep, that is about right for a quarterwave. As I understand it, you have a whip antenna perpendicular to the board, sticking up 8". And you want to mount it on one of the board edges.
So, something on your board is either transmitting, or receiving, the 315 MHz energy. Lets say that it is an IC with a port that says "to antenna" on it. That same chip will have ground connections. You want to run a trace on the top of the board, as straight as possible, directly from that antenna port to the center pin on the RP connector. Just as importantly, you also need to run a much wider path of metal (maybe 1" wide minimum) on the backside of the board, without any interruptions, directly between the ground pins on the IC and the outer shell of the RP connector. People love to cut this ground plane with DC power and digital signal lines, but DON'T DO IT! Once you cut the ground plane, all bets are off.
Your antenna will have some directionality. Nothing you can do about that, unless you have a 16" diameter ground plane and you put the antenna right in the middle of it. My experience with such edge mounted antennas is that most azimuths you will be within 5 dB on antenna gain ripple, and there might be one or two azimuths where the gain may dip as much as 10 dB.
Try to get as much continuously connected ground plane on the back of the board as you can. If you skimp on ground plane surface area, you will have poor radiation efficiency, AND the antenna may detune itself (not resonate at 315 MHz anymore).