How to sort index of a Series when index is months

Question

Here is my Series

Date
April        389
August       406
December     350
February     361
January      333
July         389
June         400
March        383
May          417
November     372
October      383
September    406
Name: Data_Value, dtype: int64

I want to sort this so the index becomes January, Fenruary, March.... I tried this code:

df.index=pd.to_datetime(df.index, errors='coerce')
df = df.sort_index()

I got this output:

Date
NaT    389
NaT    406
NaT    350
NaT    361
NaT    333
NaT    389
NaT    400
NaT    383
NaT    417
NaT    372
NaT    383
NaT    406
Name: Data_Value, dtype: int64

How can I fix it?