Get integer row-index in dataframe where column matches specific value
With boolean indexing, you can slice the dataframe to get only the rows where the date equals "2016-04-13" and get the index of the slice:
df[df.Date == "2016-04-13"].indexOut[37]: Int64Index([2], dtype='int64')
With the uniqueness assumption, there will be only one element in that array, so you can take the 0th element:
df[df.Date == "2016-04-13"].index[0]Out[38]: 2