Lucky deduction, but looking back, I believe what they were going for is what she should have been vaccinated for at 6 months of age (since there are no apparent symptoms).
Hep B vaccine is usually given at birth, 1 month, and 6 months of age, so it's pretty important that she be vaccinated against it, unless she already has it, in which case she should be treated to avoid cirrhosis.
The only infection on that list that you would even screen an otherwise healthy appearing individual is HepB. The others I would think you only check if the patient has a presentation that makes you suspect them, like EBV if they had signs of mono, or RSV if they had respiratory symptoms. At that point, they're no longer screening tests, but more diagnostic ones.
the child is asymptomatic because hepatitis B is mostly silent in infants due to poor lymphocyte system. other diseases would probably show more symptoms
Disorders common in east Asia according to Goljan:
EBV infection - mostly leading to nasopharyngeal CA
Nitrosamine linked Intestinal type gastric CA
In this question, since the patient is asymptomatic and EBV isnt exactly "screened for", went with HepB as the answer
To sum it up, even if you didn't memorize the whole immunization table, it's easy to remember HBV immunization is done at birth, 1mo, 2mo and 6mo roughly. Also added that the baby is of East Asian decent, and the fact that other infections on the list aren't screened for in the first place in healthy-looking patients, I think it's safe to deduce HBV was the answer here.