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One thing to keep in mind is that Missouri's muzzleloader deer season runs from December 17th through December 27th. While pressure and activity in the field is nothing compared to the regular firearms season, it's vital to practice safety in the field, especially if hunting on public land. It's always the right thing to do to wear blaze orange when rabbit hunting anyway, but a must when venturing out during muzzleloader season.
There are many great public areas to hunt rabbits in Missouri. If you have beagles or some other rabbit dog, check and make certain the area you are in allows them. For example, Bush Wildlife area has specials regs for hunting rabbits in general and especially with dogs. Visit mdc.mo.gov for specifics.
If you want a heads up on locating some of the better rabbit hunting conservation areas, visit the page HUNTING RABBITS ON MISSOURI PUBLIC LANDS. There you'll find great basic information on what to look for in identifying rabbit habitat. Also, there you will find a list of conservation areas with good rabbit hunting in each of Missouri's geographical regions.
Using this research, you should be able to find an area within a one county drive or so. If you want to look for some other areas, visit the Missouri Public Land Hunting Page. Towards the bottom, you will find a link to pages where conservation areas are listed by county. Also, the availability of various species are identified. You can quickly tell whether a given conservation area has good rabbit (as well as most other game species) hunting or not. Also, the size of the area is given as well as a link to the MDC page for that area. We feel it's an area that every Missouri Outdoosrman or Outdoorswoman should have bookmarked for regular use.