You can use to_period("Q"):
df.index = df.index.to_period("Q")
import pandas as pd
df = pd.DataFrame({"y": [1,2,3]},
index=pd.to_datetime(["2000-03-31 00:00:00", "2000-05-31 00:00:00", "2000-08-31 00:00:00"]))
df.index = df.index.to_period("Q")
df
To convert a normal column col, use dtto access the objects Datetimein the series:
df = pd.DataFrame({"y": [1,2,3], 'col': pd.to_datetime(["2000-03-31 00:00:00", "2000-05-31 00:00:00", "2000-08-31 00:00:00"])})
df['col'] = df['col'].dt.to_period("Q")
df