Welcome to the forum. I just noticed that you are a medical doctor. None of us here is a doctor, except for one member who treated for HCV but doesn't come around much and another who is a scientist (HR, who also doesn't come around much).
As Bill said, there's about a five percent chance of vertical transmission but I don't know if the risk is greater through c-section or vaginal birth, although I would guess the former. I'm quite sure breastfeeding poses no problem, as HCV is strictly via blood-to-blood contact.
Anyone with HCV should be immunized for HBV and HAV, if no antibodies for these are present.
Studies are limited in pediatric hepatology. You can have a look at this thread, which concerns a new member discussing the tx of her eight-year old son:
I took a peek at your interests that you listed in your profile and was somewhat blown away. What area of medicine do you focus on?
Your interests are very impressive: allergies, epilepsy, migraines, thyroid disorders, alternative medicine, eye care, nutrition, weight management, arthritis, family health, pain, diet and nutrition, osteoarthritis, rheumatoid arthritis, children's health, genetics, parenting, back pain, chronic pain, fibromyalgia, headache, pediatric pain, exercise and fitness, weight loss surgery, women's health, asthma, autoimmune disease, lupus, multiple sclerosis, Parkinson's, bladder diseases, incontinence, overactive bladder, HIV/Aids, heart health, arrhythmias, cholesterol, deep venous thrombosis, heart disease, pet health, cats, dogs, other pets, pregnancy, beauty, fertility/infertility, menopause, trying to conceive (TTC), urinary tract infection, cancer, breast cancer, cancer treatments, chronic myelogenous leukemia, head and neck cancer, lung cancer, ovarian cancer, prostate cancer, skin cancer, diabetes, high blood pressure/hypertension, Hepatitis C, infections, kidney disorders, men's health, smoking, sleep disorders, insomnia, restless leg disorder, skin conditions, acne, eczema, psoriasis, sexual health, senior health, Alzheimer's disease, longevity, osteoporosis, diabetes gestational, diabetes Type 1, diabetes Type 2, digestive health, colitis, acid reflux/GERD, Crohn's, nighttime heartburn, emotional health, ADD/ADHD, anxiety, bipolar disorder, depression, schizophrenia, continue medical education, paediatrics, internal medicine, med spec/Interest, general surgery, medical laboratory, nephrology, autoimmune, chest physician, general cardiology, echocardiology, obstetrics & gynecology, reconstructive plastic surgery, child and adolescent psychotherapy, psychiatrics, ENT, neuro-opthamology, neuro-opthamologyl, pediatric opthamology and pharmacology.
Wow. You are certainly a high-achiever! Congratulations on your broad interests. Do you specialize in obstetrics?