Does Licking The Cat's Milk Bowl By An 18-month-old Lead To Rabies Transmission?

Question : 10 days back i fed a stray cat by pouring a glass of milk in cats bowl.. im not sure if the glass touched cats bowl or some droplets spilled on the glass.. my daughter who is 18 and half months old exactly after an hour picked the glass from the table and put it in mouth.. what are the possibilities of rabies transmission here. does she need booster dose now? It is exactly 5 months since she received her 4 dose of rabies vaccine in october for another nonbite exposure... this time out of anxiety i took her to my pediatrician and insisted her for a booster dose but she said boosters are recommeneded only after a year and that rabies is not a routine vaccine and there would be many side effects.. as far as i read 2 Booster doses are recommendd after the second exposure right.. am i putting my daughter at risk.. is there a time frame in which boosters are not required for the second exposure.. i know exposure is highly unlikely in my case.. but me being a paranoid mom want to ease my mind by understanding the logic here.. does my daughter who is just 1 and half years old have enough immunity against rabies without a booster?

Doctor you have already responded to my query few days back clearly in the best possible way but i am getting haunted by the same thing everyday.. i know i need a psychiatrist but please bare with me n answer the following questions: Does she not require a booster beacuse of the kind of exposure where there is no risk of transmission or boosters are not needed within a year for any kinda contact? Would she require a booster if she had been bitten or scratched? What does it mean wen they say transmission through mucous membrane.. saliva getting in eyes and mouth?

It means no booster is required within a year for any kind of transmission.. thanks in advance for putting up with my questions.