Can I create a separate Catalina partition on an external disk and just boot into it when needed?

Yes, you can do that. It is best to use an external drive, preferably an SSD. When you get the new drive plug it into your Mac. Open Disk Utility. Click on "View", then "Show All Devices". Select your new drive in the Disk Utility sidebar. Choose the drive media itself, not the indented volume below it. Click on "Erase". In the dropdown select Scheme: GUID Partition Map, then Format: APFS. Click on "Erase" in the dropdown. Let Disk Utility finish. Your new drive should now be ready to install macOS Catalina.

Download the Catalina installer from the App Store in step 4 of this Apple Support Article. How to upgrade to macOS Catalina - Apple Support When it opens, choose your newly formatted drive as the destination for the Catalina installation. When it is finished installing on your new drive you should be good to go. When you want to start up in your Mojave drive again, just click on "System Preferences", then "Startup Disk", and choose your Mojave drive.

fuzzy has provided some excellent information above. I would like to offer some additional thoughts. If you prefer not to change the selected start up drive in System Preferences, instead, you may press the keyboard's Option key when you start up the computer and in a bit it will give you a screen which allows you to select the alternative operating system on an each time basis. I did what you are suggesting before I upgraded to Catalina, installing Catalina on my external drive to test it. When I initially got the drive, I partitioned it into two partitions, one smaller one for the Catalina OS and the other partition is used to physically duplicate and back up all of my other files. It is always kept up to date, right to the minute, so I will never ;lose any data if my main hard drive ever fails. Good thinking.