Olympic ice dancing champion Meryl Davis and her newlywed husband, Fedor Andreev, just finished their three-day destination wedding in the South of France — and there are no plans to turn around and throw a baby shower just yet.

“We’ve talked about it,” Davis, 32, tells PEOPLE of starting a family with Andreev, 37. “But it’s a little bit of a ways away.”

“Fedor and I have made no secret in our conversations together that we always talk about how we’re kind of late bloomers,” she explains. “While we absolutely love spending time with our friends’ kids and our cousins and family’s kids, we’re not quite ready.”

The couple, who wed on Saturday night in Provence after some nine years together, joke that they are already parents to one “fur child”: their 2-year-old mini sheepadoodle, Bilbo.

“We definitely feel like a little family unit already, and so once we feel like we’re ready then it’s going to be another discussion,” says Andreev. “But I kind of have a feeling it’s going to be another furry one before non-furry one.”

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Raising a dog isn’t bad practice for the real thing, either.

“It’s interesting parenting a pet with your significant other,” Davis says. “I feel like you learn a lot about yourself … but also we’ve learned so much about each other, and I think it’s made us just fall in love with each other even more — watching each other co-parent and sort of figuring out how to be a team. Not just the two of us, but in taking care of something else.”

“I mean I know that sounds silly,” she says, “but it’s just such a great way to continue growing and evolving together and appreciating each other’s special qualities.”

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After their weekend wedding festivities ended on Sunday night, Andreev and Davis remained in Provence, where they married in the backyard garden of Le Mas des Poiriers, to soak up a few more days with their families.

They have a honeymoon planned for later this year. Davis, who said in 2017 she would not continue competing, still tours extensively with longtime skating partner Charlie White. Andreev, an accomplished skater in his own right, now works as an entrepreneur.

The future awaits.

Says Davis: “We’re just excited to continue going on adventures together.”

For more on Davis and Andreev’s destination wedding in France, subscribe now to PEOPLE or pick up this week’s issue, on newsstands Friday.

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