computing an EWMA of a DataFrame by time

You need two things, ensure the date column is of dates (rather of strings) and to set the index to these dates.
You can do this in one go using to_datetime:

In [11]: df.index = pd.to_datetime(df.pop('date'))

In [12]: df
Out[12]:
              avg     high   low    qty
date
2013-05-27  16.92    19.00  1.22  71151
2013-05-30  14.84    19.00  1.22  42939
2013-06-02   9.19    17.20  1.23   5607
2013-06-05  23.63  5000.00  1.22   5850
2013-06-10  13.82    19.36  1.22   5644
2013-06-15  17.76    24.00  2.02  16969

Then you can call emwa as expected:

In [13]: pd.ewma(df["avg"], span=60, freq="D")
Out[13]:
date
2013-05-27    16.920000
2013-05-28    16.920000
2013-05-29    16.920000
2013-05-30    15.862667
2013-05-31    15.862667
2013-06-01    15.862667
2013-06-02    13.563899
2013-06-03    13.563899
2013-06-04    13.563899
2013-06-05    16.207625
2013-06-06    16.207625
2013-06-07    16.207625
2013-06-08    16.207625
2013-06-09    16.207625
2013-06-10    15.697743
2013-06-11    15.697743
2013-06-12    15.697743
2013-06-13    15.697743
2013-06-14    15.697743
2013-06-15    16.070721
Freq: D, dtype: float64

and if you set this as a column:

In [14]: df['ewma'] = pd.ewma(df["avg"], span=60, freq="D")

In [15]: df
Out[15]:
              avg     high   low    qty       ewma
date
2013-05-27  16.92    19.00  1.22  71151  16.920000
2013-05-30  14.84    19.00  1.22  42939  15.862667
2013-06-02   9.19    17.20  1.23   5607  13.563899
2013-06-05  23.63  5000.00  1.22   5850  16.207625
2013-06-10  13.82    19.36  1.22   5644  15.697743
2013-06-15  17.76    24.00  2.02  16969  16.070721