I don't know why no one is answering your question, so here goes.
No you do not have to put rebar in the footer, just like there is no law that is requiring you to put gas in your car. Of course if you want to drive the vehicle, then the laws of physics will eventually compel you to add gas.
Likewise, the cost of rebar is so minimal to the overall construction expense, that it simply becomes a very cheap form of insurance.
Two pieces of .5" bar evenly spaced near the bottom of the footer, sitting on a few evenly space bricks, is easy to do. I have also placed the concrete first and then set the rebar on top and tamped it down with a rake.
The only concern with a variable depth footer is that the minimum thickness is sufficient to carry the load. I helped a guy poor a footer for his house. He ordered too much concrete and by the time we got around to the garage area we had about 4 extra yards that he could send back to the plant or use it in some way. He formed the ends of the trench around the garage and filled the garage footer up over 2 feet thick. His response was "there are worse places to waste concrete than in your footer"
The extra thickness is only hard on your wallet, nothing more.
From experience, a sloppy footer ends up making a sloppy foundation, which ends up making a sloppy building. Can't really explain why, but that is how it goes almost every time.