Just install FileMaker Pro on the new machine. There are no special operations other than that that you need to do.
There is no CD drive on the MacBook Air. Can't "just install".
I seem to remember something about having both machines on the same WiFi network, then allowing sharing of the drive in the MacBook Pro. That way you can use the drive of one machine to install on the other (Air). This assumes you still have both machines.
There are any number of ways that you can install, it's just a matter of moving the install files onto media that your computer can access.
If your machine has a USB port, you can copy the installer files from the CD to a flash drive.
If you can connect to a network, you can share the CD drive on the another computer and then access and run the installer over the network starting from your new machine.
You can also copy said files across the network to the new machine's hard drive and run the installer from it.