I purchased the Group 34 Extreme Battery for my 2010 4Runner. I purchased the Rago Fabrication battery box to all this size battery. The group 34 and group 31 extreme batteries may need an aftermarket battery box.
I researched the sizes of the batteries and this is what I found prior to purchasing the battery and then the battery box. I do not know what size battery the FJ uses.
Group 31 batteries are relatively large and powerful batteries, featuring 20h capacity in 75-125 Ah range, providing 750-1250 CCA, 150-250 minutes RC etc.
The size is a group 34 battery is also large. The physical dimensions are 10.25 x 6.8125 x 7.875 inches. This translates roughly to 26 x 17 x 20 cm. In terms of actual size, group 34 batteries are smaller than group 27 but are larger than similar group 31.
I am extremely happy with battery although the cost with the battery box was more expensive than getting the battery from an auto parts store.
You may want to check the battery size of your FJ and review the dimensions provided for the battery considered on the Odyssey Battery Website.