Yes, you can shoot rimfire to qualify. Please note that if all you are going to shoot is pistol caliber carbine (.22LR, 9mm, .40, etc), you do not need the rifle permit and can shoot those on pistol lanes.
NRA certified RSO, Pistol/Rifle/Personal Protection Inside The Home instructor, Certified SIG/Glock pistol armorer. Any question, please feel free to sent e-mail to firstname.lastname@example.org
or visit our forum on Calguns under vendor section!