Preview:
qs = df['Quarter'].str.replace(r'(Q\d) (\d+)', r'\2-\1')
qs

0    1996-Q3
1    1996-Q4
2    1997-Q1
Name: Quarter, dtype: object

df['date'] = pd.PeriodIndex(qs, freq='Q').to_timestamp()
df

   Quarter       date
0  Q3 1996 1996-07-01
1  Q4 1996 1996-10-01
2  Q1 1997 1997-01-01
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