The “Slide Away” singer, 26, and her rumored girlfriend were spotted on a lunch date in Los Angeles on Sunday with Cyrus’s mom Tish.
In photographs of their outing, Cyrus wraps her arm around Carter’s shoulder as both women, wearing matching white t-shirts, smile.
“They live together and are very happy,” a Cyrus source tells PEOPLE. “Miley is doing great. She is moving on. She seems to have no regrets. She loves being with Kaitlynn.”
Things between the two have been heating up since mid-August, when news first broke that Cyrus had called it quits with husband Liam Hemsworth.
Shortly after, she and Carter, who recently split from husband Brody Jenner, were spotted kissing on an Italian getaway.
Since returning to Los Angeles, Cyrus and Carter have been seen together on multiple occasions, including at last week’s MTV Video Music Awards in Newark, New Jersey.
MTV cameras briefly caught Carter, 30, placing her hand on Cyrus’s head backstage before the singer performed an emotional version of her break-up anthem “Slide Away.”
Later, the two were photographed holding hands as they walked into the Up and Down nightclub in New York City after the show.
“Miley is very close with Kaitlynn. It’s romantic, but also a friendship,” an insider previously told PEOPLE. “They are both going through similar stuff right now and are bonding over it.”
Cyrus and Hemsworth announced their separation in a statement in August, just seven months after tying the knot following an on-again, off-again relationship of 10 years.
“Liam and Miley have agreed to separate at this time,” began a statement from the couple’s rep, exclusively obtained by PEOPLE on Aug. 10. “Ever-evolving, changing as partners and individuals, they have decided this is what’s best while they both focus on themselves and careers. They still remain dedicated parents to all of their animals they share while lovingly taking this time apart. Please respect their process and privacy.”
Hemsworth, 29, filed for divorce on Aug. 21, citing “irreconcilable differences.” The pair signed a prenuptial agreement ahead of their marriage, so a smooth divorce is expected, PEOPLE confirmed.
“She didn’t expect it and is a bit disappointed, but she is still doing well and has obviously moved on as well,” a Cyrus insider previously told PEOPLE.