Judd, 34, explained that her daughter hates having curly hair - and "screams at the mirror" that she wants locks like her mother.
"She's got this brush and she's started standing in front of the mirror and she brushes and brushes her hair," Judd explained.
"She's got this curly hair, so she brushes it and it springs back up. And she screams at the mirror, she's like, 'arrgh!'.
"She's just furious."
"I said 'Billie what are you doing, just let it go babe you've got curly hair' and she says
'Mummy I don't like my hair I want straight hair like you'."
Judd, who is a mother-of-four and married to former Carlton AFL Captain Chris Judd, said that while on holidays in Port Douglas, her daughter didn't want to go to dinner because she didn't feel as beautiful as her mum.
"We were going out for dinner, and I had these cool studded flats on," she explained.
"She [Billie] had these little flats with a pussycat on them.
"We were just about to walk out the door she goes, 'Oh mum, I can't go out for dinner, you look far more beautiful than me'".
Co-host Monty Dimond joked that perhaps Judd's good looks were "ruining" her young daughter.
"Bec, you've got to ugly yourself down ... your looks are ruining this child," Dimond suggested.
Judd was quick to respond, assuring listeners her daughter doesn't have much screen time - and she can't even read yet.
"I don't know what's going on," she said.
"She doesn't get screen time, she's not watching shows that would put any importance on appearance.
"She's not on Instagram, she can't read for goodness sake."
In May, Judd revealed how having twin boys in September had resulted in "twin leftovers" which she had to get cosmetically removed.
Judd explained on her KIIS FM radio show that her legs started to show popped blood vessels - a visible change she hadn't experienced during her first two pregnancies with Billie and Oscar.
"I think just carrying the twins around and the pressure on my legs ... Every day I could almost see new blood vessels just popping and little veins all over my legs. I'm just getting rid of the twin leftovers.
"I don't think I will ever get rid of my weird sticky-outie belly button, but at least my legs will look normal again."
Judd is no stranger to body shaming, and was criticised during her most recent pregnancy for being too slim.
"You are a freak. How can you be carrying twins and be that thin lol," one person wrote alongside an Instagram snap of her bump.
"WTF, so skinny, I'm surprised her doctor didn't confront this," another added.
Following the birth of her boys, Judd decided to disable comments on her Instagram page in a bid to gag trolls who constantly commented on her "skinny" frame, for looking "extremely sick" or for being a bad role model for other mums.
In response to an article written about her slender frame in 2016, Judd penned a scathing blog post criticising the publication for calling her "scary skinny".
"Healthy comes in all shapes and sizes," she wrote. "
Some people are naturally thin, some people are naturally bigger, some people are more athletic in tone, some people have minimal tone.
"We are all different and we are all NORMAL. This is the message we need to project, not 'Is Rebecca Judd a bad role model for being thin?' Seriously?"
Judd said she and her husband have started focusing more on other qualities to try and change her daughter's new found obsession with appearance.
"I'm not beautiful when I don't have makeup on - I'm not beautiful," Judd said.
"She's such a gorgeous little girl, but it really makes Chris and I think OK, we've got to put so much emphasis on being a kind human and be strong and being smart."
"Girls, they are tricky!"
