I know how you can export your calendar but I do not know how you can synchronise your Google Calendar to another of your Gmail accounts.
There's a help article from Google about sharing a calendar with another account: https://support.google.com/calendar/answer/37082?hl=en
You can share the main calendar for your account, or another calendar you created.
- On your computer, open Google Calendar. You can't share calendars from the Google Calendar app.
- On the left, find the "My calendars" section. You might need to click it to expand it.
- Hover over the calendar you want to share, click Options and then **Settings.
- To share with individuals: Under "Share with specific people," the email address of the person you want to share with.
- To change wider sharing settings: Under "Permission Settings", choose an option in the drop-down menu.
- If someone isn't already added, click Add person.
- Click Save.
If you shared your calendar with an individual email address, they'll see your calendar in their "Other calendars" list. If you shared your calendar with an email group, they'll see the calendar in their "Other calendars" list once they click on the link in the email invitation from Google Calendar.