Up until what age can a lady fall pregnant or have babies? I am 34 years old and don't have babies yet

Risks for any pregnc. At 34 you are not too old for babies. Many consider the rate of Down syndrome births as a marker for age & childbearing. Risks are lowest in the early 20's at about 1/2000 with a gradual increase in risks that hit 1/100 at 40 & 1/12 at 50.There is a baseline risk of about 4% of an unexpected outcome with any pregnancy. The ds risk must be added as age related risk. Discuss with your doc.
Into the forties. Women are having children into theirearly and mid forties. Good luck.