This is a lengthy answer, sorry!
The chance of the virus being transmitted to the baby is 5-10%. Pregnanacy with Hep C is not officially discouraged.
http://www.hepcbc.ca/pregnancy.htm
Pregnant patients with hepatitis C should be advised to:
Obtain vaccination against hepatitis viruses A and B as indicated.
Abstain form alcohol use.
Avoid hepatotoxic drugs such as acetaminophen (Tylenol) that may worsen liver damage.
Inform the infant’s pediatrician of the mother’s hepatitis C status.
Not donate blood, body organs, other tissue, or semen.
Not share any personal items that may have blood on them (e.g., toothbrushes and razors).
Discuss the low but present risk for transmission with their partner and discuss the need for counseling and testing. However, HCV-positive persons with one long-term, steady sex partner do not need to change their sexual practices.
Liver enzymes and PCR should be obtained at the beginning of pregnancy, and as needed thereafter
The following recommendations from The Society of Obstetricians and Gynecologists of Canada may be helpful in counseling women considering amniocentesis.
SOGC Recommendations
“Amniocentesis in women infected with hepatitis C does not appear to significantly increase the risk of vertical transmission, but women should be counseled that very few studies have properly addressed this possibility.
In HIV-positive women all noninvasive screening tools should be used prior to considering amniocentesis.
For women infected with hepatitis B, hepatitis C, or HIV, the addition of noninvasive methods of prenatal risk screening, such as nuchal translucency, triple screening, and anatomic ultrasound, may help in reducing the age-related risk to a level below the threshold for genetic amniocentesis.
For those women infected with hepatitis B, hepatitis C, or HIV who insist on amniocentesis, every effort should be made to avoid inserting the needle through the placenta. “
Delivery and Postpartum
The risk of vertical transmission of HCV appears to be related to the level of viremia in the pregnant mother and not to the route of delivery. The virus does not appear to be transmitted when a woman's titer is < 10^6/mL or is negative. Although Tejari et al and Conte et al did not find cesarean section to be protective against transmission of HCV to the neonate Gibb et al have found the HCV maternal to child (MTC) transmission rate to be reduced in patient delivered by elective cesarean. The latter study has yet to be confirmed. Elective cesarean to reduce MCT transmission of HCV is not presently recommended by the Centers for Disease Control, American Academy of Pediatrics or the American College of Obstetricians and Gynecologists. At delivery staff and the baby’s pediatrician should be notified of the mother’s hepatitis C carrier state.
Breastfeeding does not appreciably increase the risk of transmitting HCV to a neonate.
http://www.perinatology.com/exposures/Infection/HepatitisC.htm