Yes, Gwyneth’s daughter really is the Apple of her eye

Gwyneth Paltrow could be the glowing, golden poster child for first-time motherhood.

Over the past year, the Oscar-winning actress secretly married musician Chris Martin of Coldplay and in May gave birth to their daughter, Apple Blythe Alison, after 70 hours of labor.

“It’s just the most incredible thing that’s ever happened to me,” says Paltrow, 31. “I’m just amazed at how much I love her.

“It’s totally cliched. You wake up every morning with the feeling like it’s Christmas morning. You can’t wait to see them and see what they’re going to do and just hang out with them, and it’s just the best.”

So much so that Paltrow has no plans to ditch diaper changes for movie sets any time soon.

Aside from “Sky Captain and the World of Tomorrow,” a special-effects-driven action-romance which opened Friday, and the drama “Proof,” already wrapped and opening in December, she has no films lined up.

“I just want to be home right now and not commit to doing anything that’s too big of a part,” says Paltrow, who doesn’t have a nanny. “I’m feeling very much like I want to be with my daughter.”

As for the infant’s name, the subject of much heated debate in the media?

It was Martin, 27, who picked it, Paltrow says.

“We were just kind of pregnant; we didn’t know (the sex of the baby), and he said, ‘I think if she’s a girl we should call her Apple,’ ” she explains.

“And I just love the name, because I thought it just conjures such nice sweetness and wholesomeness.”

She pauses and breaks into laughter. “I loved it, and it seemed to cause such a scandal in the world! I don’t know really why.”

Today she’s radiant, but Paltrow shudders when she recalls the debilitating queasiness she felt during her early pregnancy.

She was in London shooting “Proof,” the film version of the Broadway hit in which she plays a devoted daughter grieving over the death of her genius mathematician father (Anthony Hopkins).

“Luckily, I only threw up a few times, but I was incredibly nauseous,” she says. “I wouldn’t even take Tylenol while I was pregnant. I’m this nerd who is not putting chemicals in my body.”

Being back on the publicity circuit for “Sky Captain” is a pleasant change of pace, Paltrow says.

“It’s like the first time I got my hair blow-dried. I’m wearing heels again,” she says. “This is fun. I get to pretend to be a grown-up again.”

Paltrow and Martin, who is British, split their time between New York and London, where they have homes.

“I think, until (Apple) starts kindergarten, we’ll probably travel a lot,” Paltrow says.

“Her father will be on tour a lot, and I’ll be with them, and we’ll all be together. Maybe she’ll go to school in New York.”

And maybe she’ll have siblings.

“Not now or anything, but, yeah, I think so. My brother’s so important to me, and I can’t imagine not having a sibling. But I’m just loving to be with her.”

Paltrow pauses, laughing as she jokingly continues to map out Apple’s life: “And then she’s going to go to Harvard. And then, will be a doctor.”

Or, perhaps, an Oscar winner like Mom or Grammy winner like Dad.

The birthday bunch

Actress-comedian Anne Meara is 75. Actress Sophia Loren is 70. Actor Gary Cole is 48. Actress Kristen Johnston (“3rd Rock From the Sun”) is 37. Singers Gunnar and Matthew Nelson (Nelson) are 37. Drummer Rick Woolstenhulme (Lifehouse) is 25.