Can I travel outside of Thailand with a re-entry permit after getting my Non-O visa stamp?

You can travel anywhere, but only do a re-entry, cover your visa, and come back to renew before it expires.

You can definitely apply for a 1-year extension for the same reason as your initial visa as long as;

- you get a re-entry permit before you leave Thailand

- you will be back before your current stamps (permitted until stay on initial Non-O visa and re-entry permit) expire

- meet the all requirements in time

A re-entry permit would NOT add any day to your current stamp, freeze the time when you are out of Thailand, or "push" back the due date to later than your current extension stamp. You have to be back in Thailand within the "permitted up to" date on your stamps. Your extension will be invalid when the 'permitted until' date passes. A re-entry permit cannot help it.

@Andy *******

yes just purchase at the airport

Yes, you can travel internationally by getting a re-entry permit before your departure. Be sure you are back in Thailand within the current stamp (and enough days to prepare the necessary documents)..