Boosting the Analogue Response of a Sensor
Yes, an op-amp is the way to go.  Properly bypassing power to the sensor will help.  You're trying to use such a small portion of its range, though -- that's usually a plea to the Electronics Gods to "please smite me".

So proceed, but see if the sensor has a noise specification.  Also carefully check the sensor's rated offset voltage, and the degree to which that offset voltage is expected to change with temperature.  My intuition tells me that you can pretty much count on having to adjust for offset, and that it would be a very good idea to breadboard a prototype, and test it over your anticipated temperature range.