'Honey Boo Boo' Star: Sorry Baby Girl ... It's Birthing Time!!

Anna "Chickadee" Cardwell -- Mama June's oldest daughter -- has been ready to pop with her 2nd kid for days now, but no dice ... so, she's hoping doctors can get it done.

Anna tells TMZ she's going to the hospital early Wednesday for an induced labor. She's been having contractions off and on for more than a week.

Mama June won't be at the hospital ... we're told she'll be home babysitting Cardwell's 3-year-old daughter. TMZ broke the story ... 21-year-old Anna announced the pregnancy in April. She and husband Michael are expecting a girl and plan to name her Kylee.

Score another one for the Kardashians.