Lana Del Rey is super proud of her wedding ring … showing off her new jewelry on a date with her alligator tour guide husband, Jeremy Dufrene.

The “Summertime Sadness” singer couldn’t stop admiring her wedding ring Sunday while snuggling up to her new husband outside a restaurant in Louisiana.

Lana and Jeremy, who tied the knot Thursday in a ceremony at his airboat tour business HQ, sat down for a smoke break after breaking bread together … and they appeared to snap a couple cute selfies on her phone.

It’s the first time we’re getting a good look at the wedding ring Jeremy slipped on Lana’s finger … the diamond looks pretty big, and it’s visible from afar.

Lana and Jeremy totally look like they’re in the honeymoon phase here … and they took time to take photos and chat with some of the restaurant staff after their meal was over.

LDR certainly looks comfortable down on the Bayou with Jeremy … and it will be interesting to see where they pop up for their upcoming honeymoon.