Do you fear you will pass your stutter on to your children?

Do you fear you will pass your stutter on to your children? I have a 16 month old boy and another coming in 3 days and sometimes I get a knot in my stomach when I think about my stutter being passed on to my children. I have no idea yet if my son has a stutter (he's 16 months) but it kills me to think that I maybe the cause of a difficult social and work life. I'm a covert stutter and I don't want my sons to have to go through the mental strain and anxiety I go through day in and day out.