Well it belongs on the right side. Adding weight when you can move the battery is well.....adding weight.
IF you expect to race that thing, you need to consult the NHRA rules, or at least the rules under which you are going to race, for needed safety concerns
I believe you either have to have the battery in a METAL box which is externally vented, or a plastic box with an added firewall behind the rear seat.
You need a battery disconnect which will ALSO KILL THE CHARGING SYSTEM so that if the switch is pushed (and it MUST PUSH, not PULL) to off, the engine will die. The disconnect must be in the positive lead, not the ground.
One easy way to do this is to buy a Cole Hearse disconnect with two large and two small connections. You can use the two large ones to break the battery, and the two small ones you can ground one, run the other up front on a small wire to operate a relay and break the ignition/ alternator field.