Palmer was born at 8:37 a.m. on Saturday weighing in at 7 lbs. 3 oz.
Eubanks called the birth of her first child the "wildest experience of [her] life" and joked that her husband is "recovering and doing well."
Pictures of the little girl in a pink hat, being held by her glowing mother and on the way home from the hospital soon racked up more than 11,000 likes within the first 20 minutes of being posted.
The Wednesday before she gave birth, Eubanks took to Instagram to post a past due notice and address her friends and fans giving her pregnancy advice.
"Yes I'm alive. Yes I'm still pregnant. Tried all the old wives tales...I'm glad that standing on your head chanting the Lords Prayer while drinking spoiled goats milk worked for you...but it ain't working for me," she joked.
Eubanks said she was nervous about becoming a mother during a 2016 episode of her Bravo show.
"I guess in a nutshell I'm trying to figure out if I am just simply not maternal or if my decision is rooted in fear or anxiety," she told a therapist. "I feel like I'm giving up something. Everybody I talk to, they say, 'Your life will change' and I think, 'But I love my life. I don't want it to change.' And so I feel like having a child is a potential for something to go wrong."
"I freak out if I'm not in control of a situation, like I have problems being a passenger in a car, unless I like, know who I'm riding with," she continued. "And I know when you have a child, like you have to give up control in your life. Just thinking about it, I start to feel anxiety."