This article concluded that, “High-dose vitamin D (1200 IU) is suitable for the prevention of seasonal influenza as evidenced by rapid relief from symptoms, rapid decrease in viral loads, and disease recovery. In addition, high-dose vitamin D is probably safe for infants.”. ~ Dr. Broussard
Utilizing a randomized, open, controlled clinical trial, a study was performed to “evaluate the clinical efficacy and safety of vitamin D” for the prevention of influenza A in infants. Infants were randomized to low-dose or high-dose vitamin D, for four months, with 200 infants in each group. Influenza A was observed in 78 cases of the low-dose group, and 43 cases of the high-dose group. (P=0.0001). In the high-dose vitamin D group, it was observed that “the median durations for fever, cough, and wheezing were shorter.” 
In both groups “viral loads showed a downward trend, but were significantly different between groups in the second and third measurements.” Adverse and serious adverse events were reported to be low or very low, and were not significantly different between the two groups. Accordingly, the “incidence of influenza A was significantly lower in the high-dose group, as compared to the low-dose group,” and “the viral loads of influenza A in infants in the high-dose vitamin D group decreased more rapidly [as] compared to those in the low-dose vitamin D” group. Thus, it was concluded that “high dose vitamin D (1,200 IU) is suitable for the prevention of seasonal influenza as evidenced by rapid relief from symptoms, rapid decrease in viral loads, and disease recovery.”
The high dose was also determined to be safe in infants.
Ref.: Zhou J, Du J, Huang L, Wang Y, Shi Y, Lin H. Preventive Effects of Vitamin D on Seasonal Influenza A in Infants: A Multicenter, Randomized, Open, Controlled Clinical Trial. The Pediatric Infectious Disease Journal. Publish Ahead of Print. DOI: 10.1097/INF.0000000000001890.