Q: Swapping Final Cut from desktop to laptop

Without the disc you stand little chance of copying it across as there are numerous hidden files scattered all over.

You could try Migration Assistant  but whatever you do, don't delete it as you will probably lose it forever.

There is no place you can legally download it.

Try eBay etc. to see if you can find a cheap copy but be aware that it may not work properly on more modern computers with the latest OS.