Kourtney Kardashian and Travis Barker Step Out for the First Time Since Getting Engaged

The Blink-192 drummer proposed to the Poosh founder in Montecito, Calif., on Sunday

Kourtney Kardashian and Travis Barker have been spotted for the first time since getting engaged.

Kardashian, 42, and Barker, 45, appeared in good spirits as they stepped out together on Monday, hours after reaching a new relationship milestone the day before.

Though her new massive oval-shaped diamond ring couldn't be clearly seen in the photograph, Kardashian wore a black hoodie and boots, while carrying a small black purse, her cell phone and a beverage.

The Blink-182 rocker wore a white T-shirt underneath a black leather jacket, which he paired with a navy beanie, black jeans and a necklace.

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Barker proposed to the Poosh founder at the Rosewood Miramar Beach Hotel in Montecito, Calif., as the sun was setting. The beachside proposal came as "a complete surprise" for Kardashian, a family friend told PEOPLE.

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"Travis told her family that he planned to propose, but everyone was great at keeping it secret," the source said. "The Rosewood is their favorite for short weekend getaways. They often stay at the hotel. This is why Travis proposed there. It's a very special place to them, but it was also easier to keep everything a secret by proposing there."

According to the insider, Kardashian is "ecstatic" to be engaged. "She can't wait to marry Travis," the source added. "She would also love to have a baby with him."

PEOPLE confirmed Kardashian and Barker's relationship in January, reporting that the pair had "been dating for about a month or two" and have "been friends for a long time but it's turned romantic." As their romance progressed, the pair didn't shy away from showing PDA on social media.

Kardashian also helped Barker overcome his fear of flying. Before they traveled internationally over the summer, he had not boarded a plane in 13 years after surviving a deadly plane crash in 2008.

"I made a deal with her that she had just said to me, 'I would love to do so much traveling with you. I want to go to Italy with you. I want to go to Cabo with you. I want to go to Paris with you. I want to go to Bora Bora with you,'" he recently recalled to Nylon. "And I said, 'Well, when the day comes you want to fly, I'm telling you I'll do it with you. I would do anything with you. And just give me 24 hours' notice.' And that's what she did."

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Barker added, "It's still something very new to me, but having something that gives me the strength and hope to be able to overcome things that were so traumatic in my life, it just says a ton. She's definitely that for me. I'm invincible when I'm with her. It's like I never dreamed, I never even considered flying again."

Kardashian shares sons Mason, 11, and Reign, 6, and daughter Penelope, 9, with ex Scott Disick. The exes split in 2015 after nine years together.

Barker, meanwhile, shares son Landon, 17, and daughter Alabama, 15, with ex-wife Shanna Moakler. They were married from 2004 to 2008.

The drummer, who was also married to Melissa Kennedy from 2001 to 2002, has remained close to Moakler's 22-year-old daughter Atiana, whom the 46-year-old model shares with boxer Oscar De La Hoya.