No, baby-mamas are of any age ... at least into their 30s. I don’t know if anyone would use the term of a woman 40+.
It’s not that she’s a Mama who’s a baby ... it’s that she’s the Mama OF a baby. Same with “baby-daddy.”
I have gained this wisdom through getting to know the cashiers at my local Walmart. One girl stopped me one day on my way out so I could help another girl figure out her due date!