I know LOTS of women who have had babies over the age of 35 and they were all perfect babies. I know 3 people who had babies when they were under the age of 30 and they had babies with downs syndrome.
My doctor said that those numbers are largely inflated and that though the risk may be slightly higher that the likelihood a healthy baby will be born in much greater. Additionally, in other countries, they do not do special testing on older moms until they pass age 40.
Personally I would not have a baby at 44, but that is just me. Kudos to those who make that choice for their own lives.