Yes, this is the right place to ask. Moveit can certainly do this, but it will require a URDF before it will work. The URDF file is how moveit knows how your arm moves -- e.g. how long each link is and what kind of joints connect the links.
Once you have a URDF creating the SRDF is pretty straightforward -- 15 minutes or so with the tutorial.
With that you will be able to use KDL (built into moveit) to do inverse (and forward) kinematics. KDL is a numeric solver and there may be faster ways to do inverse kinematics (depending on how your arm works), but KDL is generic and easy to get working.
We have some tutorials on how to do inverse/fwd kinematics once you have a URDF and SRDF
-Acorn