First of all, it is illegal to sale a pistol across state lines. You will have to show proof of residency. You can get the firearm the day (or day after) you get your drivers license switched.
There is no law in Kentucky specifically saying it is illegal to discharge a firearm on private property. The only way I can see you running into problems is if your property is within a city's limits.
Lastly, if you are serious about firearms (I assume you are) then you did not move to the wrong state. Kentucky's laws are very straight forward and very relax (compared to much of the US, especially Illinois).
Welcome to the forums.