I am 39 years old and have two healthy children, ages thirteen and ten. Do you recommend taking additional testing? I am thirteen weeks pregnant.
What you're talking about is testing for chromosomal problems. This is a philosophical decision, in that you have to decide whether or not you're willing to possibly put a normal baby at some risk by undergoing an amniocentesis to make sure there is no indication of Down syndrome or other problem. Many pro-life expectant couples decline the test as it wouldn't change anything they would do anyway.
Although it's considered good prenatal care, the philosophical aspect of the test makes it your decision. The statistics after age 35 start getting worrisome, which is why you're being offered this option.