Current Sensing with Op-Amp, do I need a shunt resistor in series with the load on the output?
What it will do is basically waste power, since the opamp will do its best to modify it's output to make the negative terminal to the postive one. So you'll still get 10V on the load, there will still be a voltage drop on the 100mΩ resistor and a slight amount of power wasted. 

So you don't need it. One thing you might need is a resistor between the opamp and the transistor because you might exceed the output current on the opamp. Or if the opamp output can source a lot of current, you might exceed Ib on the transistor, so make sure neither of those situations doesn't occur. Another problem with these circuits is they can become unstable at high frequencies, especially if there is a cable adding inductance on the load, so watch out for that.  

A useful thing to do  with this circuit and a variable load is to use the shunt resistor for current measurement.