"We're grateful for the prayers of thousands," Jim Bob Duggar tells PEOPLE as he and wife Michelle left Arkansas Children's Hospital on Tuesday with Josie. "We are so happy," adds Michelle. "We are so excited, we are running on adrenaline. I have been getting into the routine of every three hours feeding, diapering and taking her temperature. We are so encouraged that she is doing so well."
As they drove away from the hospital, her physician, Dr. Robert Arrington said, "This is the first time Josie has seen sunlight." She was born on Dec. 10 via emergency C-section at just 25 weeks' gestation. Weighing just 1 lb. 6 oz., the micropremie fought for her life, surviving a bowel perforation at only 8 days old.
Today, Josie weighs 4 lbs. 9 oz., is breathing without oxygen, eating every three hours and stable enough to go home, says Arrington. It's a bittersweet day for the staff. "I will miss being around the baby and the family," Arrington says. "They are very nice people. But they've told me they will stay in touch and come by the nursery to let us see her."
Michelle says the family's emotional roller-coaster ride has "leveled out," and that Josie's disposition has been a joy in hard times. "She has a strong personality," Michelle says. "She is a spunky little thing and will keep us all going."
The littlest Duggars at home – Jackson, 5, Johanna, 4, Jennifer, 2, and Jordyn, 15 months – have never seen Josie in person and "are jumping up and down that they will finally get to meet their baby sister," says Michelle. Of course, given Josie's still-delicate state, "the little ones will have to be careful with slobbery kisses to prevent any colds and sniffles," Michelle adds.
The family will remain in a rental home nearby in Little Rock indefinitely until they are ready to take Josie home to Tontitown, Ark. "I will be her main caregiver," Michelle says, "and we'll have a lot of helpers around to take turns feeding her and getting her to sleep."
19 Kids and Counting: Josie Comes Home airs Sunday, May 9, at 8/7 Central on TLC.