You definitely don't want to remove the existing brick unless you want to build a new frame. The brick around the existing firebox adds some support, but more importantly helps with the draft of the smoke. Without the brick you could get smoke into the room.
You can easily apply thin stone veneer over the existing brick area. Additionally, you can add Durock to the existing brick if you want to widen out the fireplace.
You have made good decision to remove the dated stone. Let us know how the finished project turns out.
Below is a transformation of removing a very dated stone and replacing the stone with a new and more contemporary still stone.
If you would like more ideas on other stone fireplace pictures look at the link.