I am a structural engineer and I can confirm that Raymond's recommendation for a 6" thick slab is certainly sufficient for a hot tub. The only suggestion that I would give would be to thicken the slab at the perimeter to be 12" deep by 8" wide with a continuous #4 bar centered in the thicked portion, 3" clear from the soil. I would also agree with Raymond that the slab should have a layer of 6X6 W1.4XW1.4 welded wire mesh reinforcing which should be supported during the pour so that it is in the top 1/3 of the slab.
small footer is fine, but its only a slab for a hot tube , not a house: