Tom & Katie's Baby Girl!

At nearly nine months pregnant, many women start wishing for that due date to just arrive already: Sleeping is a pain, breathing a chore and any hope of seeing your feet has vanished. But breezing through a Beverly Hills shopping blitz-without fiancé Tom Cruise-in her final days as a mom-to-be, Katie Holmes proved that her retail stamina, at least, was going strong. Still, if checking out designer clothes that far along in a pregnancy is a little like visiting Italy on a no-carb diet-so many temptations, so few choices-Holmes managed a couple of purchases that signaled she was looking ahead to postmaternity fashion freedom: a pair of cuffed black hot pants and sky-high strappy gold heels.

As it turns out, she won't have to wait too long to slip into the fun stuff: On April 18 Holmes, 27, and Cruise, 43, welcomed their first child, a 7 lb. 7 oz. baby girl named Suri, at an L.A.-area hospital. (In an only-in-Hollywood twist, Brooke Shields, who last year sparred with Cruise over her use of medication to treat postpartum depression, delivered her own newborn girl down the hall from Holmes the very same day.) Both Holmes and Suri "are doing wonderfully," Cruise's rep tells PEOPLE. "The baby is happy and healthy. Katie is doing great. Everything is fantastic."

The birth went so smoothly, in fact, that Holmes left the hospital within 24 hours. A source close to the actress's Toledo, Ohio-based family, who were vacationing in Florida at the time of the birth, says that new grandma Kathy Holmes, 59, "was crying and said, 'We have a sweet baby girl! We're so excited!'" Holmes opted for an epidural, says the source, adding, "Everything is fine and Katie can relax now." As for Suri-whose name the couple, in a statement, traced to the Hebrew for "princess" and the Persian for "red rose"-"she has lots and lots of dark hair and big, blue eyes," says the source. "She's going to be a beautiful baby."

Now that she's here, what's in store for the newest Cruise? An upbringing in Scientology, for starters. "You can be Catholic and be a Scientologist. You can be Jewish and be a Scientologist. We're just Scientologists," Cruise told Diane Sawyer on the April 14 Primetime, noting that he and Holmes (who was raised Catholic) will hold a Scientology naming ceremony but not a Catholic baptism. Explains Greg LaClaire, the vice president of the Church of Scientology Celebrity Centre International in Hollywood, which Holmes visited regularly throughout much of her pregnancy: "We have a naming ceremony at which the parents and godparents pledge to give good care while at the same time providing the child an opportunity to grow and choose their own path in life. The child is welcomed by the congregation."

Of course, Suri-who, like Cruise's kids Connor, 11, and Bella, 13, will be schooled using Scientology's "study technology"-also can expect plenty of attention. The big sibs (whom Cruise adopted with ex-wife Nicole Kidman) have already been tapped to pitch in. "The kids will have different responsibilities and run in shifts," Cruise told GQ. "They're going to help on every level. I don't think this kid's gonna be able to walk until they're about 15. Feet aren't gonna touch the ground!"

Naturally, the pampering isn't stopping there. In March, Holmes ordered three luxury bassinets from high-end baby bedding line Lulla Smith along with 30 sets of Sea Island cotton sheets. ("That baby is not going to use the same sheet twice!" jokes designer Carol Smith.) And the baby booty has been pouring in too, including a onesie that declares "Tom Coos" and a terry-cloth robe with the word "MOVIE" above a gold star.

Even as the news of the glamor girl's debut sparked a renewed frenzy at casa Cruise in Beverly Hills-circling helicopters, hordes of paparazzi and even a K-9 police unit-the new parents are making every effort to create a peaceful environment away from prying eyes in keeping with Scientology beliefs about maintaining calm around children. But Suri might want to get that passport ready: Although Cruise cleared his Mission: Impossible III publicity schedule immediately after the birth, he's likely to resume it-possibly with his two newest leading ladies in tow-before long. "Tom does everything 150 percent," says his friend Kirstie Alley, "and fatherhood he does 300 percent. They're going to have a great kid."

PHOTO (COLOR): A ROSE BY ANY NAME | Suri comes from the Middle Persian word "surika," meaning red rose, says UCLA language scholar M. Rahim Shayegan. The name "is more rare these days," says Shayegan. "More mothers and grandmothers had it."

PHOTO (COLOR): FOR SURI | Among Suri's gift haul: whimsical babywear a friend of the couple's bought at boutique Kitson.

PHOTO (COLOR): Holmes picked up one small $850 Lulla Smith bassinet and two large versions at $1650 each.

PHOTO (COLOR): SHOP TILL YOU POP! | Just before Suri's delivery, Holmes went on a three-day Beverly Hills shopping spree, picking up everything from men's jeans and sneakers (which she wore on April 15) to Lanvin ballet flats.

PHOTO (COLOR): "I know his other children very well and they are just the best, fun, well-mannered, smart kids," pal Kirstie Alley says of Connor and Isabella (with Cruise and Holmes on March 10). "You have to attribute part of that to parenting."

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By Michelle Tauber; Allison Adato; Lycia Naff, Los Angeles; Alexis Chiu, Los Angeles; Tom Cunneff, Los Angeles; Jed Dreben, Los Angeles; Julie Jordan, Los Angeles; Amy Keith, Los Angeles; Elizabeth Leonard, Los Angeles; Brenda Rodriguez, Los Angeles; Alison Singh Gee, Los Angeles; Frank Swertlow, Los Angeles and Barbara Sandler, Chicago