The "Alfie" star has spoken out about her beloved child for the first time, appearing to be smitten with the tot, reported Us magazine.
"She's so cute... She's screaming upstairs. My brain doesn't work," said Miller.
But despite her lack of sleep the 30-year-old's new role is obviously suiting her judging from her happy tone.
Miller's sister Savannah let her daughter's name slip when she took to Twitter after the birth of her niece to gush in a similar way.
She wrote, "Marlowe I love you..."
News of Miller's pregnancy broke in January, and the actress was spotted wearing an engagement ring from actor partner Tom Sturridge a month later.
Miller and "The Boat The Rocked" star, 26, were dating for over a year before the pregnancy and engagement news broke.
More From This Section
While Miller is making the most of her quality time with Marlowe for now, she looks like she'll soon be back at work.
She has already filmed a remake of Alfred Hitchcock's iconic film "The Birds" as she plays his muse Tippi Hedren in a new BBC2 biopic to be screened in September.