Even something as simple as a cold can translate into something dangerous for an infant. I wouldn't trust that my "immunity" transfer through the placenta and breastmilk would be sufficient to keep my newborn safe.
I'm also 38 weeks along, and am in California. Here, we've had an outbreak of whooping cough this year that has been particularly dangerous for infants. They are offering immunizations for mothers and fathers immediately post-partum to prevent any possible exposure to the babies. In that particular case, symptoms seem like a bad cold/cough to adults, and parents and caregivers are unknowingly the primary source of transmission to their babies.
Having said that, even with just a basic cold, I would talk to your baby's pediatrician right after delivery & get her recommendations on how to prevent infection. Likely, they'll recommend some basics like: frequent hand washing, don't cough or sneeze on your infant (which seems obvious, but you might have to remind your daughter), and being really careful about handling anything that goes into your baby's mouth (bottles, pacifiers, your breast, etc.) and making sure those things aren't exposed to your germs. It'll be important for all of your family members to take the same precautions. If your cold is really bad, maybe your ped will recommend a mask for when you're breastfeeding, when you're in such close proximity that you'd risk sneezing/couging and transmitting.
Note: I don't mean to sound paranoid - do what makes sense based on how sick you are, just like you would to prevent passing the flu around your house. Wash your hands, don't kiss your baby on the lips, don't blow your nose & then breastfeed without washing your hands. Practice good hygiene and make sure the other people in your household do too. If you've got a horrible cough or respiratory infection, take additional precautions.
I hope you all get & stay healthy & that you have a great delivery! :-)