There are a great many more exemptions to the prohibition on transport of a handgun.NRA-ILA.
Carrying and Transportation in Vehicles
It is unlawful for any person without a permit to wear or carry a handgun, openly or concealed, upon or about his person. It is also unlawful for any person to knowingly transport a handgun in any vehicle traveling on public roads, highways, waterways or airways, or upon roads or parking lots generally used by the public. This does not apply to any person wearing, carrying or transporting a handgun within the confines of real estate owned or leased by him, or on which he resides, or within the confines of a business establishment owned or leased by him.
Some include transporting to a gun shop, a target shoot, hunter safety class, and more.
Folks need to look at the statute, see the earlier links, to determine when they may transport legally.