If you want to move everything LANDesk has an executable called CoreDataMigration.exe in the ManagementSuite directory. Never tried it, don't know how well it works, but it is there. I believe that is what LANDesk runs during an install (at the end when you can check to migrate settings from another core).
There is also a paid product from Managed Planet called Database Doctor that does that as well.
Read the Best Known Methods Document:
This should cover everything you need for the most part.
Steps to move the LDMS database:
This talks specifically about moving the DB if you need to.
Post Install Backup Whitepaper:
This covers what you will want to manually backup on the core.