Let's start with a circuit that works: -
The output equals the input because the op-amp has to have both inverting and non-inverting inputs at the same voltage. OK choose an op-amp that has low Vos and low Vos drift. Choose an op-amp that has a very low noise figure if the sensor circuits you are feeding are used for very small measurements.
Your circuit - It won't work - you have placed gain into the feedback loop of an op-amp and it will sing and scream with oscillations because op-amps aren't designed to have extra gain like this. Where is the extra gain coming from? The MOSFET is common source into a load resistor. Its gain is drain resistance divided by source resistance. You have zero source resistance and your drain is 100 ohm. Need I explain more?
Emitter follower - You need to supply 1 amp to your sensors and using an emitter follower with a gain/Hfe of say 50 means your op-amp is having to feed 20mA into the base - this should not be a problem given that your supply voltage is 12V and you only need to produce 3.14V. However, you will have a power dissipation problem. 1A through the transistor with about 9V across it means 9W of power given off as heat.
Lower the power rail - I would strongly urge you to run the circuit from a lower power rail like 5V. Then you'll find that the power is only about 2W and a moderate heat-sink will do the job.
But beware - there are now extra problems in doing this. You'll find that the BJT is working closer to saturation and maybe the gain will drop to 20 meaning the drive from the op-amp will need to be as high as 50mA. Most op-amps won't do this so you'll have to find one that does. I'd start by looking at the AD8605 - it can source +/-80mA and will be nearly rail-to-rail with more normal loads like 10mA. It has fairly low noise too. Vos might be a little high though for your application.
MOSFET source follower - Alternatively use a N channel mosfet instead of the BJT - this requires virtually no drive current from the op-amp - downside - pick one with fairly low Vgs(threshold) or you won't get the output from the op-amp high enough to properly turn it on under heavy load conditions.