In Chapter 16 Wickham hears Mr Collins talking of Lady Catherine de Bourgh and he asks Elizabeth about how intimately acquainted he is with the family. Her response was "Lady Catherine de Bourgh," she replied, "has very lately given him a living. I hardly know how Mr. Collins was first introduced to her notice, but he certainly has not known her long." (bold highlights mine). Therefore confirming the thought that it is a shorter (couple of months) rather than longer time (six months); I suspect Elizabeth may have heard a great deal of detail in the time Mr Collins had spent with her family!