“My schedule is really busy, but I’m working really hard now to have more space later," Aidy Bryant says about having kids in the future

Aidy Bryant is already an Emmy-nominated comedian, but the Saturday Night Live staple would love to add one more title — mom.

“I definitely want to have kids,” Bryant, 32, who’s also the co-creator, producer and star of Hulu’s Shrill, says in the latest issue of PEOPLE. “My schedule is really busy, but I’m working really hard now to have more space later.”

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For more from Aidy Bryant, pick up the latest issue of PEOPLE, on newsstands Friday

For now, Bryant, who married her longtime love — writer and performer Conner O’Malley — in 2018, says she and her husband are still enjoying newlywed life.

Image zoom Conner O’Malley and Aidy Bryant Aidy Bryant/Instagram

“I feel like his family is my family and he feels like my family is his family. So it feels nice to be able to say that more officially,” she says, adding, “I love his family so much, and he’s really close with my parents and my brother. So, I think part of it feels more official in that way. Like the unifying of the families.”

The pair, who have been together for more than 12 years, first met while they were performing at a theater in Chicago.

Image zoom Aidy Bryant and Conner O’Malley Aidy Bryant/Instagram

“It was the first show I had ever done at that theater and he had been performing there for a long time,” she says.

“It’s not like your super traditional comedy club, it’s a lot more avant-garde and a little closer to performance art. It kind of pushes boundaries. And so, we both performed in a show there one night,” says Bryant. “Then it just so happened that we saw each other the next night at a different comedy club, and then he asked for my number and the rest is history.”