The episode showed Dannielynn's love for dancing and playing with stuffed animals.
"I think here, in Kentucky, I think it's normal as you can get," Birkhead said. "She loves school. She loves her friends. I just hope she dreams big and accomplishes a lot."
Dannielynn was just four months old when Smith, a model, actress and television personality, died of a drug overdose at age 39 in February 2007.
Birkhead subsequently battled Smith's then-partner, Howard K. Stern, and Smith's mom, Virgie Arthur, for custody.
"The problem is that people think that I'm a bad guy because I don't want Anna's mom to see Dannielynn and that's actually not the truth," he said.
"Anna's mom has seen Dannielynn, and she's seen her a few times. I say that only because I want the story to stop."
Birkhead, who met Smith at the Barnstable Brown gala in 2004, told Us Weekly in May that Dannielynn was pushing him to find a date at the annual event.
He said at the time that the gala is the only night of the year he goes out.
"When I was leaving, Danni said, 'Would you do me a favor at the party?' And I said, 'What?' And she said, 'Would you get yourself a date?' I looked at her and started laughing and she said, 'No, really, I'm serious,'" he recalled.
"I pulled up to the party and she was texting me, 'Are you there yet? Did you get a date yet?'" he said.
"It's funny she's kind of at the point right now where she's kind of encouraging that."
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