I need a collar for my new dog, but I can't get them from the pet store. I can pick them out from the buy menu and my sim does the complete purchase animation (going to the cashier, handing over money) but no money is deducted from my account and the collars don't appear in my inventory.

Do you do the change appearance thing in the mirror on the dog? (I dont have it yet, but am assuming that is how you put them on) and does it show up then? Or am I being completely ignorant here?

They dont' appear in your inventory. Send your sim home and lick on a mirror, it should say "Change the appearance of [your pet]." Collars should be one of hte options.