The app is just needing some time to determine what the date is and display it in its icon in the Dock. If you close Calendar and then reopen it does it still take a second or so to display the correct date?
How much RAM do you have? Have you installed or run any "cleaning", "optimizing", "speed-up" or anti-virus apps on your Mac?
Boot into Safe Mode by booting with the Shift key held down and check there to see if the problem persists. Reboot normally and test again.
NOTE: Safe Mode boot can take up to 10 minutes as it's doing the following;
• Verifies your startup disk and attempts to repair directory issues, if needed
• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)
• Prevents Startup Items and Login Items from opening automatically
• Disables user-installed fonts
• Deletes font caches, kernel cache, and other system cache files