The best way to migrate data for MacJournal to a new machine is to use the built-in data migration utility that the Mac provides. When you set up a new machine, you can connect it with an old Mac and have it copy all the data over automatically. This will get MacJournal's data wherever they are and provide the easiest switchover experience.
If this is not an option, you can copy MacJournal data from one machine to another to use it on the new machine. If you still have access to the old machine, open MacJournal and open the Preferences window. Click on the Advanced toolbar item at the top of the window. Click on the "Reveal in Finder" button to show the main MacJournal data file in the Finder. This is the file that you need to copy to the new machine. There are many ways to accomplish this, such using file sharing, or a file storage service such as iCloud Drive.
Once you get the MacJournal Data file to the new machine, you can double-click it in the Finder to open it in MacJournal. This will open it as a second window in MacJournal. If you use the "Reveal in Finder" button in the Advanced preferences on the new machine, that will show you the file that you want to replace with the data from the old machine. Quit MacJournal and then replace that file with the file that you copied (either placing that file in the Trash or letting Finder replace it when dragging the correct file into that folder). When you launch MacJournal again, it should open up the right data file from the old machine and things should look how they did on the old machine.