February 07, 2018 01:53 PM

Kylie Jenner and Travis Scott are focusing on one thing and one thing only right now: their baby girl.

A source tells PEOPLE that the couple is “over the moon” after welcoming their daughter Stormi Webster on Thursday — but they’re in no rush to take the next step in their relationship.

“Kylie and Travis are not officially living together,” says the insider. “He has his own place. They are co-parenting though, and things are going great. They are together and happy.”

According to the source, Jenner, 20, and Scott, 25, still have no plans to get married.

“They’re not in rush,” says the source. “They’re just enjoying their little family.”

The source adds that the rapper “has been great” with the baby and is “very sweet with his daughter.”

Kylie Jenner and Travis Scott in May 2017
INSTARimages.com

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The couple have been dating since April 2017, after Jenner split from her on-again, off-again boyfriend of nearly three years, Tyga — and a source recently told PEOPLE that her relationship with Scott is very different.

“Kylie had a lot of trust issues with Tyga,” explained the source. “He was her first love and she was obsessed with him, but she never felt like she could trust him 100 percent. With Travis, things got really serious fast, even though she was still getting over Tyga.”

Kylie Jenner and Tyga
Gilbert Carrasquillo/Getty Images

According to the source, Jenner’s relationship with Scott has helped her grow.

“He’s very protective of Kylie, and his family embraced her, too,” the source said. “Kylie has matured a lot since becoming pregnant. She’s much less dramatic than when she was with Tyga.”

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