Moving Quicken and data files to a new Mac

Yes, you can just download a fresh copy of Quicken from the website. There are other ways, but that would be the easiest.

The safest way to move your data file is to make a backup on the old machine (menu File > Save a Backup). Move that file to the new machine and restore it. The backups are compressed and that ensures there will be no macOS permission errors on the new file. 

That should be all you need to do. You may need to reset some app-level preferences in Quicken such as how many auto backups to make. You could move the preferences file too, but it may be easier to just check that the preferences on the new machine are set the same as the old machine (menu Quicken > Preferences).