Don't use Perl. Perl is not the best choice for all uses. Booting from a floppy and running in a limited environment is one of them. Perl is an interpreted language. Compiling it to binary code is hard. The perlcc is experimental. The perlcc docs says: "Use for production purposes is strongly discouraged."

Some of the solutions suggested, like PAR and TinyPerl, package the interpreter and your script into an arhive which is unpacked at run-time. The Perl interpreter is big and you will have a hard time squeezing it down to fit on a floppy. Also, there may not be a place to unpack the archive.

Also, there is a big difference between running Perl under Windows and DOS. There is a DOS port, but my impression was that it requires a 32-bit compiler and runtime environment. DJGPP is most often used.

I bet you don't need an interpreted programming language for your application. Doing it in C would make the most sense and make it easy to fit on a single floppy.