How can I treat my 11 month old with conjunctivitis?

Depends. It depends if its allergic, viral or bacterial. If its viral then its similar getting a cold it takes its course. Treatment will be cold compressors, and artificial tears. Hand heygiene is very important to avoid spread of it. If its bacterial it needs antibiotic treatment. It requires doctor visit. If its allergic it will be itchy and teary. It needs allergy drops and cold compressor.
See her doctor. Conjunctivits in infants is not something to try treating on your own. Although some forms may not be infectious, those that are can cause serious damage if untreated. This should be evaluated by a general or pediatric eye doctor.