Fox News White House Correspondent Peter Doocy and White House Press Secretary Karine Jean-Pierre shared a laugh over Doocy’s promise to name his new baby after either Jean-Pierre or President Joe Biden.

Doocy is married to Fox News and Fox Business correspondent Hillary Vaughn, and the couple have expecting a daughter for months. At  White House briefing in January, Doocy joked about the impending bundle of joy, quipping that he’d name her “Josephina — for the President,” then when Jean-Pierre suggested “Karine” for a name, said “We’ll take it under advisement.”

At Thursday’s briefing, Jean-Pierre welcomed Doocy back for his first briefing since the blessed event, and drew laughs by asking after “baby Karine”:

MS. JEAN-PIERRE: Zeke, before I go to you, I forgot to tell Peter to welcome back and congratulations on being a dad. And how is baby Karine doing? She’s doing good? (Laughter.)

ED O’KEEFE: Ha! (Laughter.)

MS. JEAN-PIERRE: Ed — (laughs) — Ed had, like, this delayed reaction.

PETER DOOCY: It’s — I — I do have a lot of hard questions for her when I get home. (Laughter.)

MS. JEAN-PIERRE: Oh. Are they hard or are just — are they seriously hard or — (laughs) —

PETER DOOCY: You tell me.

MS. JEAN-PIERRE: I don’t want to say the next word that I want to say to that. (Laughter.) Okay, I’m —

PETER DOOCY: Thank you.

MS. JEAN-PIERRE: Zeke, the floor is yours.

ZEKE MILLER: Thanks, Karine. And welcome back, Peter.

Doocy is a new father, but he did not name the baby “Karine.”

Bridget Blake Doocy was born Feb. 1, and was the subject of an exclusive People Magazine photo spread. In comments to the magazine, Vaughn joked her new post as mom is not much of a change:

“I didn’t realize this until now, but I’ve been training for motherhood my entire career by trying to get lawmakers on Capitol Hill to respond to my questions. This job isn’t much different,” the new mom tells PEOPLE. “‘Baby Bridget – can you give us a comment? Are you hungry or gassy, or both?’ Trying to get an on-the-record answer is tough!”