Miley Cyrus & Liam Hemsworth Go Back to Work

06/07/2012 at 07:00 PM EDT

Miley Cyrus and Liam Hemsworth Engaged and Back to Work
Miley Cyrus's photoshoot and Liam Hemsworth on set
Bauer-Griffin; Splash News Online

Miley Cyrus

Miley Cyrus

One week after getting engaged, Miley Cyrus and Liam Hemsworth are back at work but in separate cities.

On Wednesday, Cyrus, 19, hit the beach in Malibu for a magazine photoshoot. She's also writing songs for her next album, and will be in the studio in the coming weeks, a music source tells PEOPLE.

Hemsworth, 22, is in New Orleans where he's been shooting his upcoming film Empire State with Dwayne Johnson and Emma Roberts.

But don't expect Cyrus and Hemsworth be apart for long. "Even when they're working, they find time to be together," says another source.

Right now, the couple are enjoying being engaged and haven't dived into wedding planning yet. "She's playing that part by ear," adds the source.

For more on Cyrus and Hemsworth's engagement, including what their families think, pick up this week's issue of PEOPLE, on newsstands Friday

Additional reporting by JD HEYMAN

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