Contact your city inspection department to see if you need a permit.
A load bearing wall that is there for support of something above it will usually run the length of the structure and perpendicular to the ceiling joists and there will be headers/beams over any openings. Just being perpendicular to the ceiling joists doesn't make it load bearing as most bedroom and bathroom walls can run every which way but aren't designed as such for load bearing. I doubt seriously that a 3' wall as you describe is load bearing unless it is attached to headers over the open spaces and you would notice a header/beam extending on to another wall.
Watch out for any electrical wires or plumbing before you go willy nilly cutting into the wall with a reciprocating saw. Look in the basement and in the attic above this wall for wires and pipe. It might carry a plumbing vent from below which would then have to be moved.
You are also going to have to fix the ceiling and floor to match when the wall and cabinets are moved.
By the way, Amy, where did you do new installations before?