Once they lose their spots I do not consider them fawns...we then call them "this years deer." I looked up the definition of fawn from Merriman-Webster and get the following:

Function: noun
Etymology: Middle English foun, from Middle French feon, faon young of an animal, from (assumed) Vulgar Latin feton-, feto, from Latin fetus offspring -- more at FETUS
1 : a young deer; especially : one still unweaned or retaining a distinctive baby coat