I'm not really sure most repliers replied to the right question in the original post. You've all guided him on how to build a GOG style installer application, but not actually playing Carmageddon on a modern system without the CD with the CD music intact.
That's an entirely different and much more complex issue.
With Carmageddon being old enough, one solution isn't too hard to do - as it was a game with both DOS and Windows code on the same disc, you can make an image of the CD, and make a Dosbox setup that will auto-mount the CD image to let you install and play the game with the music as if you had the CD in the drive. For Windows programs that is much harder to do - Daemon Tools does exist, which allow you to mount CD images in Windows, but if you have that installed it could conflict with a lot of modern DRM-heavy games, which check for Daemon Tools and other popular virtual disc programs and won't run unless those programs are uninstalled, even though you own a legal copy of the game and don't run the disc through virtualisation.
GOG games that use CD images in Windows use proprietary programs for that, probably a combination of changing the actual game, and using GOGWrapper or some other part of the GOG game install to handle the virtualisation. I do not know which program they use for that, if they even use something that isn't in-house.
For Carmageddon your best bet is to just use DOSBox, the setup would be one time only, then you can just copy the folder around - make a bin/cue image of your Carmageddon disc, set up your preferred directory structure (make an empty folder with an easy name and path to use as the root hard drive for Dosbox, make a subfolder named CD or something like that and copy the CD image there. Start DOSBox and mount the root folder as C (i.e. mount c C:\DOSBOX), and write imgmount d "carmageddon.bin" -t iso -fs iso, then go to the D:\ drive, write INSTALL or what the DOS install command for Carmageddon was, install the game as you would using the game's default path, to DOSBoxes virtual hard drive, and there you have the base install done.
Next you open the dosbox.conf file that came with your Dosbox install, and at the end of the file (below the [autoexec] line) you put the commands that will be issued at the moment you launch Dosbox, something like:
[i]mount c C:\DOSBOX
imgmount d "carmageddon.bin" -t iso -fs iso
C:
cd CARMA
carma.exe (or what the name of the DOS executable was, I don't remember it right now)
exit[/i]
These lines will automatically mount your virtual hard disc and carmageddon CD, and start Carmageddon, and then close Dosbox when you exit the game, pretty much the way GOG does it. You can then copy the Dosbox folder anywhere you want and run the game automatically from that folder.