Johannah Faith Duggar was born at 6:30 a.m. Tuesday and weighed 7 pounds, 6.5 ounces.
The baby's father, Jim Bob Duggar, a former state representative, said Wednesday that mother and child were doing well.
He said Johannah's birth was especially exciting because it was the first time in eight years the family has had a girl.
Jim Bob Duggar, 40, said he and Michelle, 39, want more children.
"We both just love children and we consider each a blessing from the Lord. I have asked Michelle if she wants more and she said yes, if the Lord wants to give us some she will accept them," he said.
The Discovery Health Channel filmed Johannah's birth and plans to air a show about the family of 18 next May.
The Learning Channel is doing another show about the family's construction project, a 7,000-square foot house that should be finished before Christmas. The home, which the family has been building for two years, will have nine bathrooms, dormitory-style bedrooms for the girls and boys, a commercial kitchen, four washing machines and four dryers.
Jim Bob Duggar, who sells real estate, previously lost his bid for the U.S. Senate. He said he expects to run for the state Senate next year but isn't ready to make a formal announcement.
Michelle Duggar had her first child at age 21, four years after the couple married.
Their children include two sets of twins, and each child has a name beginning with the letter "J": Joshua, 17; John David, 15; Janna, 15; Jill, 14; Jessa, 12; Jinger, 11; Joseph, 10; Josiah, 9; Joy-Anna, 8; Jeremiah, 6; Jedidiah, 6; Jason, 5; James, 4; Justin, 2; and Jackson Levi, 1.