This is not what pandas.query is supposed to do. You can look at package pandasql (same like sqldf in R )

Update: Note pandasql hasn't been maintained since 2017. Use another library from an answer below.

import pandas as pd
import pandasql as ps

df = pd.DataFrame([[1234, 'Customer A', '123 Street', np.nan],
               [1234, 'Customer A', np.nan, '333 Street'],
               [1233, 'Customer B', '444 Street', '333 Street'],
              [1233, 'Customer B', '444 Street', '666 Street']], columns=
['ID', 'Customer', 'Billing Address', 'Shipping Address'])

q1 = """SELECT ID FROM df """

print(ps.sqldf(q1, locals()))

     ID
0  1234
1  1234
2  1233
3  1233

Update 2020-07-10

update the pandasql

ps.sqldf("select * from df")

Reading a file in Python

Here's how to read in a text file in Python.

query_filename = 'C:\Users\Admin\Desktop\Python\Open Source\query.sql'
# 'rt' means open for reading, in text mode
with open(query_filename, 'rt') as f:
    # read the query_filename file into a variable named query
    query = f.read()
# replace the literal string 'date_string' with the contents of the variable startDate_sql
query = query.replace('date_string', startDate_sql)
# get dataframe from database
query_result = pd.read_sql(query, conn)

Using parameterized queries

You should probably avoid string replacement to construct queries, because it suffers from SQL injection. Parameterized queries avoid this problem. Here's an example of how to use query parameterization with Pandas.

The read_sql docs say this params argument can be a list, tuple or dict (see docs).

To pass the values in the sql query, there are different syntaxes possible: ?, :1, :name, %s, %(name)s (see PEP249).
But not all of these possibilities are supported by all database drivers, which syntax is supported depends on the driver you are using (psycopg2 in your case I suppose).

In your second case, when using a dict, you are using 'named arguments', and according to the psycopg2 documentation, they support the %(name)s style (and so not the :name I suppose), see http://initd.org/psycopg/docs/usage.html#query-parameters.
So using that style should work:

df = psql.read_sql(('select "Timestamp","Value" from "MyTable" '
                     'where "Timestamp" BETWEEN %(dstart)s AND %(dfinish)s'),
                   db,params={"dstart":datetime(2014,6,24,16,0),"dfinish":datetime(2014,6,24,17,0)},
                   index_col=['Timestamp'])