Ground Plane Layout for Power Supply on PCB
Looks good, keep the ground plane the same. Grounds should be seperated for noise or isolation, otherwise it can cause problems. The ground needs to be the same, otherwise the circuit would not function,as the current would not flow back to the source.


  Is this OK or should I do something differently in the design such as
  separating ground for the battery pack and the rest of the circuit?


You should not do something different, you should have one ground plane, it should be on the bottom layer. If you can't put it on the bottom layer, whatever your design does, ground should be as continuous as possible, if you have large currents (over 1A) then use a PCB trace size calculator to find out if there will be issues. You may want a few stitching traces (to tie ground together). If that truly is the design you end up with.