Nicole Kidman and Keith Urban had an unwelcome welcoming committee as they winged into Sydney, Australia, on Wednesday night with month-old daughter Sunday Rose.

The Daily Telegraph reports that a crowd of reporters was waiting at the airport to capture the Down Under couple and their still-under-wraps offspring. (Bucking the big-money baby picture trend, Nicole and Keith currently have no plans to release her photo.)

The media stakeout apparently occurred despite "a carefully constructed and covert plan," which included arriving "under the cover of darkness" and using decoy vehicles and view-obstructing airline equipment.

But some enterprising photographers did manage to score the sought-after shot, with the fuzzy footage showing Kidman emerging from a private jet, cradling a bundle of blankets that appears to hold a safely tucked Sunday.

(See the blurry video of the actress's airplane exit here.)

After making their getaway from the airport, the Oscar winner and the country crooner headed to their waterfront Sydney home, where, the paper says, Kidman's doctor dad Antony met his new granddaughter for the first time.

Also rumored to be on hand for the homecoming was director Baz Luhrmann, who perhaps wanted to check on the condition of his leading lady, whose baby belly disappeared within days of Sunday's debut.

Kidman, along with co-star Hugh Jackman, is expected to start shooting a few more scenes later this week for the filmmaker's big-budget epic "Australia," which is set for release on Nov. 14.

But in between filming, she wants to stroll around her hometown with her daughter, and on Thursday she and Urban called into a Sydney morning radio show to ask the media to give them a wide berth.

"Keith and I 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," said Kidman. "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."

Added Urban, "I get the interest & But at the same time, it's our little girl. Sometimes when people come right up in your face and you think, 'Good God, would you do that to anybody else's child?' That's all."

The proud parents did reveal a few tidbits about Sunday during the chat, including which one of them she takes after.

"She looks like Keith," offered Nicole. "I think she does,"

Urban, however, isn't quite convinced, saying, "Well, she's a bit of a mix."

Some other tyke details: Sunday has "a little bit of hair" with a "bit of a reddish tint," according to Kidman, while Keith admits they're only getting about three hours sleep at a time. 

"But it's a solid three hours," laughed the singer, who appears to have embraced the joys of fatherhood.

"Anybody out there who's got kids [knows] it's just a certain kind of feeling that you can only experience when you do it," he explained. "She's just awesome ... cute little thing. I'm not looking forward to having to go on tour and having to leave."