If i do not have a family history of down's, is my baby at risk for the disease?

Yes: Risk of down's syndrome depends on the mother's age. The older a woman is the higher her risk for down's syndrome. Even young women can have a baby with down's syndrome; their risk is very low however. Similarly an older woman can have a normal baby; their risk for down's syndrome is higher.

1/590 births: As above the rate of ds births are lowest in the early 20's at about 1/2000 with a gradual increase in risks that hit 1/100 at 40.There is always a baseline risk of about 4% of an unexpected outcome with any pregnancy.This must be added to specific age related risk. A visit with a genetic counselor can identify specific risk for any couple.

Mother's age: The risk for having a child with Down syndrome is related to maternal age, more than family history.