Is the calendar set to sync to your Google account?
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You can also go to your calendar on your device and go to settings and choose which calendars are syncing to your google account, for my calendar I hit the menu button on the top left, scroll to the bottom and choose Settings, from there I get a list of the various calendars I have on my google account and I can click on each and from there choose to sync or not sync it. Depending on your device and calendar app it may be different for you but it is there somewhere.
Try going to Settings (on your device) then Accounts, hit the three dots in the upper corner and see if Auto sync data is turned on, then click on Google in the list of accounts, from there you should see your google account(s), select one and see what is set to sync to Google. If calendar is set to sync then you'll have to go to your calendar and specify which calendars you want to sync. (above menus may differ depending on your device, for instance Auto sync may be under data usage for Android 4.4 and earlier devices).
Depending on the device you are transferring to there are also applications such as Samsung Smart Switch (each manufacturer has similar software) that will allow you to transfer data directly between old and new device.