The sentence is "Parents
aren't doing or dosing this kid."
They were talking about the kid's liver problem. As mentioned in the script, liver damage could be due to hepatitis (transmitted by sex or sharing of needle) or too much alcohol.
Dosing means giving someone drugs. Perhaps it means giving the kid too much alcohol or drugs. Excessive drugs can cause severe liver damage.
Doing? My guess is having sex. House said "Hmm, daddy does seem
the type to use a rubber. So it's not viral. [He gets up and starts
pacing.] Just leaves a lot of boozerosis."
So, I guess it means the kid's parents are responsible and are taking good care of him. They didn't have sex with him or drug him. However, House never trusts the patients and he thinks everyone lies. Since the kid is autistic and can't talk, you can never be sure what the parents have done to him.
Well, this is just my guess as a non-native speaker. Hope native speakers would confirm it or give us better insight.
P.S. In general, I don't quite understand the medical terms and the diagnosis in House, but in this case, they are ove-simplifying the situation. Hep A is transmitted by food. Hepatitis B is not only transmitted through sex or sharing of needle. Open wound of Hep B carriers can be extremely infectious. Children playing together can get infected. Don't share razor blades with anyone.