Separating a circuit with existing 12-3 wiring
Yes.  This is the last person planning ahead.  They made sure you would be able to do this.  This would create a multi-wire branch circuit and you must follow the rules for MWBCs. 


There must be 240V across the hots, so neutral carries differential current not the sum of both currents. 
The breakers must have common maintenance shutoff.  It will be impossible to shut off one and not the other; one hand action does both. 


This will almost certainly have a side-effect of common trip, meaning if one side overloads, it knocks out the other side.  In fact, the most normal (idiot-proof) way to wire these is to simply use a 2-pole breaker, because they are readily available everywhere, instead of UL-listed handle-ties for those breakers, which are a specialty, hard-to-find item. 
This must not be a duplex/twin/tandem breaker, which does not have 240V across it! 

Neutrals must be pigtailed. You may be accustomed to using the two screws on each side of a receptacle for a splice to extend the circuit.  Can't do that on a neutral, because removing the receptacle etc. would then create a "lost neutral" situation downstream!  The appliances on the two half-legs would be in series with each other at 240V, and one leg could rise to as high as 240V.  


If you are past the point where the halves have split for good, then you don't need to worry about this requirement.

AFCIs normally go in the service panel, to protect wires.  Here, consult your panel's manufacturer (or the maker of UL-classified breakers for your panel) for how to do 2-pole AFCI breakers in their system.  Some simply offer 2-pole AFCI; others have you handle-tie two singles.   
There are only 2 possible places to put GFCI protection: As a 2-pole GFCI breaker at the service panel, or as a device serving only one leg of the GFCI.  You can't share the neutral past a GFCI.