If your computer with the floppy drive has a CD writer, use that to copy the game to CDR.
Otherwise, if the computer with the floppy drive has access to email, you could zip up the installer and email it to yourself.
Or if you have online storage and the computer with the floppy drive has haccess to the Internet, you could zip the contents of the floppy and store online. For example, Dropbox has free online storage up to 2 GB, which is way larger than the size of a floppy.
Or buy a USB floppy drive like one of
***these*** and attach it to a modern computer which has a CD or DVD writer. You'll be able to copy the contents of the floppy to your hard drive and then back up on CDR or DVD+R.
If the game is important to you, back it up in more than one location -- for example, on both CDR and USB flash drive -- or on both CDR and online storage.