First of all, No GPL violation here. The BIOS rom is licensed under LGPL, as long as you do not build it in the executable, you are not violating anything. Users can replace this component freely.
The disk image is formatted with "/S" option. I am not sure if that counts as shipping DOS.
You're distributing files copyrighted by Microsoft, namely msdos.sys, io.sys and possibly command.com (IIRC you could override it by setting the SHELL environment variable in config.sys).
They may be small, but they since pack the core functionality of MS-DOS, I don't know if a fair use defense would fly...
You should also distribute the source of the BIOS with the app (because Apple is the distributor, not you).
Otherwise, very cool project. Is your x86 emulator available somewhere? What will differentiate it from DOSBox?
> Yes, these files are the essential part of a boot disk. Did MS forbid people transfer boot disks when they were still selling DOS?
Do you have a license that states you can ship those "essential" files? If not, then all you have is a copyright statement, which effectively forbids redistribution.
If you can't ship an MS-DOS "format /S" image, there are several DOS clones available under open source licenses (freedos, rxdos, ...) and lots of proprietary ones targeted at the embedded market too (rom-dos, pts-dos, dr-dos, ...). You might be able to find one with an appropriate license, or buy such a license.
Another option would be to implement the DOS API (INT 21h and friends) in your emulation code, instead of within the VM as x86 code. DOSBox does this (but its emulation code would be under the GPL). DOSCMD also appears to do this and is under the BSD license: http://sourceforge.net/projects/doscmd/
The disk image is formatted with "/S" option. I am not sure if that counts as shipping DOS.