Alexa Ray Joel Has Yet to Set a Date to Marry Fiancé Ryan Gleason: 'We've Both Been So Busy'

Alexa Ray Joel may have gotten engaged to restaurateur Ryan Gleason over a year ago, but the singer has yet to set a date to say her “I dos.”

“We’ve both been so busy,” the 33-year-old daughter of Christie Brinkley and Billy Joel tells PEOPLE at the 65th birthday celebration for her mom in New York this week.

“I mean, we don’t have a date yet, but we started to plan,” says the singer-songwriter. “This is a good reminder that we have to get going on that. We always joke we want somebody like Franck from Father of the Bride for our wedding planner.”

Even without Franck, the couple has determined the baseline facts about their affair. They said they want the nuptials in New York and they want the food to be Italian. “We want that Cipriani-vibe, very New York, old-school Italian,” she says.

As for her wedding dress, that’s also to be determined. “I just want to worry about the bridal gown,” she says, noting she’s going to skip the tradition of having bridesmaids by her side. “I’m over that.”

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She said there’s one person that she’s going to tap for help with the process: Her supermodel mom. “She’s all about it,” says Joel. “In fact, I told her, ‘It’s going to be you and me doing the planning.’ She’s got great taste. I like everything antique, so it’ll be very elegant, old-world.”

And she’s planning to have her famous father sing participate in the affairs in his own special way. “He’s going to sing,” she says, noting that she sometimes joins him on stage during his Madison Square Garden monthly residency.

“We’re going to sing,” she adds. “We’re going to duet. It’s going to be like a musical. I’m always happiest when I’m singing. When I sing with Dad, it’s just the easiest thing in the world. We’ve been singing together since I was a kid, so it’s an honor to be able to just do that with him.”

As for the honeymoon, they’ve got one place in mind: “Italy, of course,” she says.

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Joel and Gleason revealed their engagement on Instagram on Jan. 1, 2018 after more than four years of dating.

“So I was completely taken off-guard, dumbstruck, and shell-shocked- and FOR ONCE in my life, I had absolutely no words, and I couldn’t speak,” wrote Joel. “I just kept staring at this ridiculously exquisite ring — and he was just hysterically laughing at me!!!”

In another photo from the exciting moment, Joel recounted the proposal, writing, “He said to me: ‘Before I met you, my world was in black and white. You colored it in between the lines.’ It was the most beautiful thing anybody’s ever said to me. How could I possibly say no to that?!?!”

Joel and Gleason also each posted a photo of the sparkler, with the latter gushing, “Luckiest guy in the world!!!!”