I am not a native speaker and yesterday someone told me that "She got her first child" would be misunderstood and "She had her first child" is correct. Now I wonder if this is a 'local' thing here in Wales or a general 'rule'.
“She got her first child” sounds like she got that child at some shop or via mail-order. Just use had there: “She had her first child before she turned fourteen.”
Note also that “to get (someone) with child” has an old-timey kind of feel to it. Shakespeare in Measure for Measure I.ii.66 refers to the punishment “for getting Madame Julietta with child”.