Upon her arrival to her hometown of Sydney, Australia, new mom Nicole Kidman asked the local media for some privacy while she shows her one-month-old daughter around town, BBC reported.

With the paparazzi eagerly waiting to snap pictures of Nicole Kidman and Keith Urban's daughter Sunday Rose, the couple, who arrived in Sydney late Wednesday night, called in a breakfast radio show yesterday, and told the hosts, Kyle and Jackie O., they are "both appealing to the press and stuff just to give us a little space so we can walk around Sydney and show the baby our town."

However, the two said they understood the interest in their daughter, "but at the same time it's our little girl," Urban said.

"She's tiny. She's like a doll, she's like a little, little thing. Just (don't photograph) right in her face or in our faces because it's scary for her," Kidman added. "Sometimes when people come right up in your face you think, 'Good God, would you do that to anybody else's child?'"

Clearly happy to talk about how their daughter looks like, the "Moulin Rouge" actress said Sunday Rose "looks like Keith. I think she does," while country superstar hubby wasn't quite so eager to agree with that, saying, "Well, she's a bit of a mix." Kidman also said the baby is already showing "a bit of a reddish tint" in her hair.

Pictures of the baby bundled up in blankets already emerged on news sites, but they are taken from far away and the baby's face is covered.

While most celebrities sell the first baby pictures for loads of money, Urban confirmed they will not be selling any of them. He also told the radio show that "We’re stoked, she’s awesome.’ Nicole adds that Sunday Rose is feeding every three hours, which probably means that Nicole is breastfeeding as formula fed babies tend to eat less often." The two are expected to release one photo of Sunday for free.

The proud parents are also eager to introduce Sunday to the family members she has not yet met. "My mother was there with me for the birth, but my dad hasn't met her and Keith's mum and dad are coming down," she said.

Kidman and Urban, who got were married in Manly, Australia in June 2006, and recently celebrated their second wedding anniversary, welcomed their baby daughter on July 7. So far, the two are busy getting accustomed with parenthood, which includes feeding the baby every three hours, which means they're not getting much beauty sleep. "But it's a solid three hours," Urban said jokingly.

The 41-year-old actress, who already has two adopted children from her previous marriage to actor Tom Cruise, has longtime spoken about her desire to give birth. She said her mother Janelle, who is a nurse and midwife, helped deliver the baby, also noting the birth was surprisingly easy, and strongly implied it was a natural birth and not a C-section.