I will second Henderson Beach as a camping spot, but with a few caveats. It will take you between 90 minutes and 2 hours (depending on route and traffic) to get from Henderson beach to the range. If you don't cut through Fort Walton Beach, you will have to cross a toll bridge (and now a toll road, I believe) to get to the range from Destin, as well. The good news is Henderson Beach is on the Gulf, and right by Wal-Mart, 2-3 miles from Destin Commons (Bass Pro, movie theater, tons of stores, Best Buy across the street), and maybe 8-10 miles from Silver Sands Outlet. Since you said you would be bringing your family, that may be appealing.
There are also campgrounds available a little farther east in Santa Rosa Beach and Grayton beach. They are quieter than Henderson, but will take a little more driving to reach shopping and the range, but you eliminate the toll bridge/road. There are plenty of great restaurants in that area, too, but they are more expensive. From the Santa Rosa Beach area, it's about 85-90 miles to K&M, with a 15-20 mile stretch of that being on I-10.
I know there are some camping areas to the north (such as Hurricane Lake, which is just a few miles from K&M) but they will be a more significant drive from the beach and major shopping, plus many of those areas have limited to no cell phone reception.
If you have any specific questions on the area (especially along the Gulf), let me know or shoot me a PM. I live in the Santa Rosa Beach/Sandestin/Miramar Beach area, and commute through Destin and Fort Walton every day.