誕生日から年齢を求めることはなんとかできますが、月齢を計算するのはなかなか大変ですよね。。
とっても簡単に取得できるパッケージがありました！作ってくれた人ありがとうございます😭
age_calculator

import 'package:age_calculator/age_calculator.dart';

void main() {
  DateTime birthday = DateTime(1997, 3, 5);

  DateDuration duration;

  // 今日が 2021-03-08　の場合。。
  duration = AgeCalculator.age(birthday);
  print('Your age is $duration'); // Your age is Years: 24, Months: 0, Days: 3

  final year = duration.years;
  final month = duration.months;
  final day = duration.days;
  return '$year歳$monthヶ月$day日'; // 24歳0ヶ月3日

  //Find out your age on any given date
  duration = AgeCalculator.age(birthday, today: DateTime(2030, 5, 1));
  print('Your age is $duration'); // Your age is Years: 33, Months: 1, Days: 26

  // Find out when your next birthday will be at 2021-03-08
  duration = AgeCalculator.timeToNextBirthday(birthday);
  print('You next birthday will be in $duration');
  // You next birthday will be in Years: 0, Months: 11, Days: 25

  // Find out when your next birthday will be on any given date
  duration = AgeCalculator.timeToNextBirthday(birthday,
      fromDate: DateTime(2021, 3, 2));
  print('You next birthday will be in $duration');
  // You next birthday will be in Years: 0, Months: 0, Days: 3

  // Find out the difference between two dates
  duration = AgeCalculator.dateDifference(
    fromDate: DateTime(2021, 1, 2),
    toDate: DateTime(2025, 5, 2),
  );
  print('The difference is $duration');
  // You next birthday will be in Years: 4, Months: 4, Days: 0

  // Add time to any date
  DateTime date = AgeCalculator.add(
      date: DateTime(2021, 1, 2),
      duration: DateDuration(years: 5, months: 2, days: 1));
  print(date);
  // 2026-03-03 00:00:00.000
}

他にも次の誕生日とかも簡単に求めることができます！！！
コードは公式からお借りしました！！
作ってくれた方本当に感謝ですーーーーーーー！！！！！！！