You have a legal right under Federal Law to transport a firearm though any state of the Union provide you take a few simple steps, such as locking it in your trunk unloaded. This is a preemptive law -- local and state governments cannot take this right away from you, the Federal law preempts all local and state governments
First, here is a topic from the BATF Site FAQ's Section:
(B7) May a nonlicensee transport firearms for sporting or other lawfulHere is the actual Federal law they refer to. I give all my friends and customer's a card with this printed on it to stick in with each firearm they are transporting just in case they need to educate local officials:
purposes?
Yes. Federal law provides a person, who is not prohibited by the GCA
from receiving or transporting firearms, the right to transport a firearm
under certain conditions, notwithstanding State or local law to the contrary.
The firearms must be unloaded and in a locked trunk or, in a vehicle lacking a
trunk, in a locked container other than the glove compartment or console.
Also, the carrying and possession must be lawful at the place of origin and
destination.
[18 U.S.C. 926A, 27 CFR 178.38]
§ 178.38 Transportation of firearms.(A good synonym for Notwithstanding is Despite)Notwithstanding any other provision of any law or any rule or regulation of a State or any political
subdivision thereof, any person who is not otherwise prohibited by this chapter from transporting, shipping,
or receiving a firearm shall be entitled to transport a firearm for any lawful purpose from any place where
such person may lawfully possess and carry such firearm to any other place where such person may lawfully
possess and carry such firearm if, during such transportation the firearm is unloaded, and neither the
firearm nor any ammunition being transported is readily accessible or is directly accessible from the
passenger compartment of such transporting vehicle: Provided, That in the case of a vehicle without a
compartment separate from the driver's compartment the firearm or ammunition shall be contained in a locked
container other than the glove compartment or console.