Quite simply the 'Jeep" had not been invented when Pearl Harbour was attacked. Indeed, it was the subsequent entry of the US into the war that spawned the contract to design and build the "reconnaisance car".
According to to the Jeep website, they had been working on protypes since WWI, got the call for the vehicle in 1940, and delivered in 1941. Since Pearl Harbor was at the end of 1941, it's pretty likely they already had the new Jeeps.
In Dec 1941 There where a few jeeps around.
The problem is that that jeeps where Slat grills and not pressed grills as in the movie.
Another slip is that the jeeps have jerry cans at the back panels (in Aug 1942 that was issued by the US Government).
There is one navy jeep (at the golf course i believe) that is a post war jeep.