If you are just going to keep it at home, you don't need to do anything.
If you want to take it off your property, you would be wise to obtain a Nebraska concealed handgun permit (CHP). Even if you don't intend to carry concealed, a CHP has significant advantages. It's somewhat expensive and time consuming but not at all difficult. Your Iowa permit is no longer valid since you are a Nebraska resident.
According to a recent decision by the Nebraska Supreme Court, a firearm inside the passenger compartment of a vehicle is considered to be concealed unless it is in plain sight or is unloaded inside a locked box. This is a problem if you drive a van, SUV, hatchback or pickup that doesn't have an inaccessible trunk. After you get your CHP, be careful about leaving your firearm in your vehicle even briefly. If none of the other passengers holds a CHP, they are guilty of carrying concealed illegally.
When buying firearms from licensed dealers (FFL), CHP holders are exempt from the NICS check.
Unless you hold a CHP, you need a "handgun certificate", issued by your county sheriff, to take possession of a handgun. Other exceptions to the certificate requirement are that the donor is a member of your immediate family, you remain within view of the donor, or you remain on the premises of the range from which you rented it.
CHP holders are exempt from Omaha's handgun registration ordinance. Everyone else needs to register before bringing the gun across city limits. This even applies to an unloaded handgun in a car trunk.
"No Guns" signs have the force of law in Nebraska. Carrying past one is legally the same as carrying concealed without a CHP. First offense is a misdemeanor; second is a felony.
