Cooper shared a slideshow of photos from her and Hudson's vacation in Turks and Caicos, including a picture of the couple on a beach and the words "It's a girl!" written in the sand.
"Blue or Pink? ...What do you think?!" Cooper captioned the post. "#BabyHudson #GenderReveal #NewMom #Yay."
Cooper announced her pregnancy in January and is due to give birth in May.
"Dear Baby, I hope you know that I already love you more than I could have imagined possible. I hope you chase all of your dreams, and I'll be there supporting you the whole way," Cooper wrote on Instagram at the time.
Cooper gave an update at 24 weeks pregnant this month, saying her unborn child is "doing great."
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"I can't believe I'm already in month 6 ahh! I feel like I still have so much to prepare, and it is very interesting watching my whole body growing rapidly," the star said.
"But I'm just so thankful that baby is doing great, and apparently about the size of a pomegranate."
"I'm doing the best I can to stay super relaxed and happy, and I think it's working," she added.
"It seems like my energy has been low and at any point I can just close my eyes and fall asleep, but besides that, everything is good!"
Cooper and Kimball got engaged in Mexico during "Bachelor in Paradise's" finale, but Kimball broke up with her one day after the finale aired due to a series of leaked text messages appearing to show Cooper had been romantically involved with another man all summer long and dating Kimball just for money and fame.
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