Miley Cyrus is making her way down the aisle – eventually.
The singer, who recently got re-engaged to Liam Hemsworth, is already "fantasizing about their wedding," a source close to Cyrus tells PEOPLE.
"They don't have a date," the source says. "They are moving surprisingly slowly. Miley seems to have matured a lot. In the past, she tended to rush things. She acts much more calm and happy now."
Hemsworth, 26, first proposed to Cyrus in 2012, but the couple later split the next year.
Last month, Cyrus, 23, was spotted wearing her Neil Lane engagement ring before PEOPLE confirmed the pair were back together.
"Liam is staying with Miley at her new Hidden Hills house," says the source. "He has been filming Independence Day: Resurgence. When Liam is off, he and Miley have spent time together at home."
The source adds that "Miley has been surprisingly low key," and that it "seems like she is trying to make sure Liam is happy."
"They haven't been out in public, because Liam doesn't like the paparazzi chaos," the insider explains.
Another source previously told PEOPLE that Hemsworth's family (which includes big brother Chris) were hesitant about the relationship in the past, but got to know Cyrus better when she spent time in Australia earlier in January.