In a clip from "19 Kids and Counting" that airs tonight on TLC, Duggar coos to her 19th child and tries to put a purple polka-dot bow on her head. Josie remains in intensive care at a Little Rock, Ark., hospital.
Born in December -- 15 weeks early -- Josie weighed just 1 pound, 6 ounces at birth. She now weighs 2 lbs., 3 1/2 oz.
"She looks so big to me," Duggar says to a nurse in the clip.
"She eats breast milk that mom has pumped and we have, and she gets it continuously at six milliliters an hour, which is about a teaspoon an hour," the nurse says.
Josie also appears to be responding to the music she listens to as therapy. "She has been very energetic," Duggar tells the nurse. "She's going to have to be to keep up with everybody at home."
Home for now is Little Rock, where the entire Duggar family relocated from their home in Tontitown, Ark., before Christmas to "be close to Josie," father Jim Bob Duggar told People magazine.
Josie Duggar was born at 25 weeks on Dec. 10 by emergency C-section, because mom, Michele, was suffering from preeclampsia.
Jim Bob told People in December that "a close friend in Little Rock has opened up their home to us for the holidays." Some of the older members of the reality-TV clan have just returned from a church mission to El Salvador, "so the whole family will be together and close to Josie for Christmas," said Jim Bob. "We're so thankful for everyone's thoughts and prayers."
In an earlier episode Michelle described how hard it had been to see her daughter fighting for her life.
"It's just very difficult seeing her struggle for life like this," she said. "I haven't really gotten to hold her yet. I'm really looking forward to the day I get to pick her up."
It's been an uphill struggle. In the weeks after Josie was born she began taking breast milk.
Freda Ruark, sister of mom Michelle Duggar, told ABCNews.com that after three breast milk feedings, Josie Brooklyn was able to keep down two.
"Josie is holding her own," Ruark said at the time. "As long as she can get some of that breast milk, that will help build up her immune system."
Ruark said there have been round-the-clock prayers worldwide and the family was focused on Josie Brooklyn getting stronger and not on why and how this happened. "Really, it is God's will," Ruark said. "There is no second-guessing."