Yeah, I think you should be fine with a 15 or 16" print. As long as you don't go below 150 PPI, you shouldn't notice much degradation. You may want to test out increasing the size in PS first. Here is what you'd want to compare:
1. Increase the size to 15 or 16 inches keeping the DPI at 300
2. Increase the size to 15 or 16 inches, but don't modify the DPI
Choose the one that looks the best. If you keep 300 DPI, PS (or what ever program you use) will resample the image filling in the "missing" pixels with its best guess. It depends on the image what will look best. If you just upload your 12 x12 for print, the image will most likely not be resampled (option 2).
Good luck.