Joel Madden whisked girlfriend Nicole Richie and their three-and-a-half-month-old daughter Harlow to the California desert this weekend for a surprise family vacation, the Good Charlotte singer tells PEOPLE

The Richie-Madden clan headed to the Palm Springs area for the Coachella Valley Music & Arts Festival, a three-day event headlined by performers including Prince, Jack Johnson and Roger Waters.

“[Nicole] hasn’t been able to do a whole lot over the year, so we’re having a little family trip,” Madden told People at the BPM Hpnotiq Smurf House, where he DJ’d a festival pre-party Saturday afternoon.

“I [rented] a house and surprised Nicole with a weekend trip because she likes Coachella. She was like, ‘I really want to go!’ So I surprised her. We brought the baby.”

And their activity? “Hanging by the pool.”

While Madden, 29, spun music for party guests including Dave Annable and Taryn Manning, a smiling, relaxed Richie, 26, chatted with friends about her daughter, who was being looked after at their nearby rental home.

Meanwhile, Joel’s twin brother Benji Madden and his girlfriend Paris Hilton, who last week celebrated their relationship’s two-month anniversary, were also in town for the music festival.

So which couple will make it to the altar first?

“We’re the family with the baby so I think probably us, but who knows,” says Joel – who remained mum on his and Richie’s wedding plans.

I have a feeling that none of these couple's would walk down the aisle...but let's see! But it has to be noted that Joel and Nicole never look like they're "in love"...they just look like, maybe two friends who have a baby together or something!

More pictures of Joel and Nicole at the Coachella Valley Music & Arts Festival. Note: Joel is seen wearing a Barack Obama T-shirt! Vote for Obama!