If the car is a 1951 and the six cylinder engine has an overdrive transmission with it, you are good to go. If you didn't have overdrive, then you would need to either add overdrive or change the rearend but if you have overdrive all you need to do is install the different exhaust header pipe and change the motor mount supports (two pieces that bolt to the cross member) and the throttle linkage. The fuel line routing is slightly different, but all you have to change is the neoprene hose that goes from the pump to the line - NAPA still sells it.
I speak from experience, having done it several times.
The four cylinder is an anemic, under-powered engine which is prone to throwing rods (I never heard of one that didn't throw a rod). If you can put a six in the car you will like it much better but be aware if you have it judged at a KFOC event there will be point deductions because there are other differences than just the engine between the standard and deluxe models. The six cylinder cars had bumper gaurds standard (many restorers have added them to the four cylinder cars as they do look better). The 1951 four cylinder cars had painted grill moulding on the hood but again, many restorers have added the chrome moulding that the six cylinder cars have (this is probably the most common modification I see on Henry Js). The six cylinder cars have stainless steel brightwork around the windsheild and rear window which the four cyls don't. The six cyl cars have two horns, the fours have only one. There are other changes too but when it comes to the engine, as long as the car has the correct rearend, the 1951 four cylinder cars all used the 41/9 (4.55:1) which is the same one used on the 6 with overdrive, it will work fine.
If the car is a 1952-53 four cylinder without overdrive, then it would have the 47/11 (4.27:1) rearend which would have to be changed.
I have a set of motor mount supports and the throttle linkage which I am willing to sell. Let me know if you're interested.