The new MBP will come with Mountain Lion pre-installed. To update the old MBP, you probably need a different source of Mountain Lion. The easier solution might be either making a backup of the old MBP with Time Machine or using the Migration Assistant of Mac OS.
With the Migration Assistant, you can transfer data and applications from the old MBP to the new one. You can start the Migration Assistant from Spotlight. Click the magnifier in the menu bar, enter Migration Assistant and hit enter. This will start a guided process to get the data to the new MBP. If you buy the new MBP at an Apple store, they might assist you in doing this.
If you prefer the backup idea, you need to get an external hard drive and connect it to the old MBP. Open System Preferences, click on Time Machine, select the external hard drive as your backup drive and turn Time Machine on.
When the backup is finished, eject the backup drive (you can do this in the Finder) and connect it to the new MBP. You can then restore user data and applications from the backup to the new MBP. Make sure the Time Machine icon is shown in the menu bar, click the icon, and choose Browse other Backup Disks. This way you can copy specific data and applications to the new computer.
AFAIK it is not possible to switch hardware in a MBP nowadays.