Before uninstalling, please verify your data is synced by checking the Web app. See here: How do I know if my data is synced?
Save a copy of the encryption key from Day One > Settings > Journals > Show Encryption Key
Quit Day One Mac.
Paste this into the Go to Folder window in Finder:
~/Library/Group Containers/5U8NS4GX82.dayoneapp2/. (See screen shots below.)
Drag the entire folder to your Mac Desktop. (This contains a local copy of your journal data backups and might be useful if any problems arise when you reinstall and reimport your data into Day One Mac.)
Drag the Day One Mac app from the Applications folder to the Trash Can.
Be sure to quit Day One Helper in the menu bar if necessary.
Go to the Mac App Store > Purchased and click Install for Day One.
Sign in to Day One Sync. Your data will download again.