Moving PDQ Inventory from one computer to another is a simple matter of copying the database files and a registry key. The files and keys to be moved are documented here. However, here's an overview of the steps to follow.
Close the PDQ Inventory console and stop the Background Service
You want to make sure that no programs are accessing the files while you copy. It's very unlikely that you will lose any data, but copying files while they're in use always entails some risk.
IMPORTANT: If PDQ Inventory and PDQ Deploy are installed on the same machine, you must stop both the PDQInventory and PDQDeploy services, preferably from services.msc.
Copy the Database File(s)
There is really only one database file, but there are some other files you may want to copy as well (they're listed below). The database is located in "%ProgramData%\Admin Arsenal\PDQ Inventory". %ProgramData% will be vary depending on the version of Windows but it will generally be either "C:\ProgramData" or "C:\Documents and Settings\All Users\Application Data".
You can just copy over the Database.db file to the new computer. You can also copy over the Backups folder which contains backups from prior versions. There may also be some backup files in the database folder (they're named with the version that was backed up, such as Database.184.108.40.206.db). There are some other files and folders you can copy as well, but they will be re-created on the new computer so there's no need.
Note: There are a couple of temporary files called Database.db-shm and Database.db-wal that you will not want to copy. It usually isn't a problem to copy them, but if they get out of sync with the Database.db file then it won't be possible to start PDQ Inventory until they are deleted.
.NET Installer File
If you downloaded the .NET installer in preferences it will be placed, by default, in the database directory named DotNetFX40.exe. Copy it over if it's there or you can download it again.
Copy the Registry Key
There is a registry key to be exported and imported on the new computer. This key holds one of the encryption keys used by PDQ Inventory and the license key (if in Pro Mode). If you don't copy the encryption key a new one will be generated and you will need to update the passwords for all stored credentials. The registry key is "HKEY_LOCAL_MACHINE\SOFTWARE\Admin Arsenal\PDQ Inventory".
Install PDQ Inventory
Make sure you are installing the same version of PDQ Inventory that exists on the old computer.
On the new computer check that the permissions set on the database folder are set to your liking. When first installed PDQ Inventory will set the directory to only be accessible to members of the Administrators group. You may need to set this manually after copying the directory.
Set the Background Service credentials
The background service will be installed with the default "LocalSystem" account and will need to be set again to the admin user you're using. Newer versions of PDQ Inventory will set this for you when you start up the console, but you will want to double-check that it gets done correctly.
Eat a cookie and enjoy a beverage
You've earned it.