Someone having a baby at 44 is not that surprising as it will be perfectly possible for some women. But fertility clinics give statistics of a 3-5% chance of natural conception per cycle in a woman of that age (compared to 25% chance per cycle for a woman in her early 30s).
Therefore for a woman of 44, she is far more likely NOT to have conceived after a year of trying, by which time she is 45 and the odds are worse still. So it's also not usual/commonplace to have a baby at 44 (though that is skewed by the fact that most women won't be trying to conceive at that age anyway).
I'm very happy for women who want to conceive in their 40s and are successful but I think it's risky to assume that "I am still having periods so I can conceive whenever I want". I really wish it was as simple as that but it isn't. I had my first child at 30, conceived straight away, no issues. Started trying for second at 35 and it took 5 years. Took a year to conceive but then had multiple miscarriages and investigations - had poor AMH levels (indicated low egg levels/poor quality eggs), progesterone too low in luteal phase so was starting to lose my womb lining before embryo embedded, uterine scarring (reduced chance for embryo to catch hold) and to cap it all an auto immune disorder with no other symptoms apart from my body rejecting the embryo as hostile. I seemed outwardly healthy and was having regular periods.
I did conceive again naturally at almost 40 and armed with knowledge of the above managed to keep the pregnancy thanks to a blood plasma transfusion.
I'm now nearly 52 and still having regular periods but I can't kid myself that I could just decide to have another baby if I wanted to (I don't and have a copper coil just in case).