As said above: FreeDOS is not an emulator. It is a complete implementation (including a complete distribution of various applications) of a DOS based operating system for the x86 platform/CPU family (I think back to the very first 8086).
There is nothing to base an emulator on here. You would
need an emulator like QEMU to run x86 code or a complete x86 operating system on the WIi.
That is precisely what DOSBox already does; and it does this quite good. The Wii versions aren't updated and not optimized and the Wii will struggle with more complex DOS games (or even trying to install DOS based 32-Bit Windows).
Are you sure about this →
I have a few PCs in active, offline usage much weaker than the Wii, but for going online they don't suffice. Whatever you have been using to post the message above is probably stronger than a Wii (or you have quite some patience with you online experience). Even the
weak for it's time 2005 laptop currently in front of me has more compute power than a Wii (the graphics acceleration if the console aside as it will probably not do anything for DOS emulation).