DR-DOS is a dedicated DOS, and is only partially open-source, but that shouldn't stop you. It is the most compatible with MS-DOS as far as the binaries go. The later versions have improvements that the original didn't have.
This is it's own flavor of DOS that runs in Windows 2K, XP, and 2k3. It is partially compatible with about 85% of the apps I have tried (not just games like they intend).
DOSemu is for Linux. You should be comfortable compiling source to be able to use this. I would suggest using another flavor of DOS other than the included FreeDOS to run on this one for compatibility.
FreeDOS is another dedicated DOS. This is the runt of the litter, but has the dedication. It has the least compatibility of all of the flavors of DOS, but is fully open-source and has the force of several developers behind it. Don't get me wrong, it has the compatibility to flash the bios on a motherboard. It is even being included on several barebones systems since Microsoft set a precedent to not include OS's on computers. This is probably the most widely available DOS.