even in the film hes had the ring for a while, even if gandalf rode all the way to minas tirith, found Isildurs scrolls then rode back to the shire again full pelt on shadowfax it would have taken him weeks (in the book frodo has the ring for 17 years before he leaves the shire).
plus hes already falling from it, he has put the ring on in the prancing pony and was playing with it before hand remember, plus on weathertop hes facing the Nazgul, whos presence & power would disturb the ring bearer greatly, and anyway look what happens to sam when he trys to fight them, he get batted aside like a pesky fly.
in other place like in Moria against the orcs/troll and against Shelob & Gollum he fights.
im not trying to change your mind legolasismyman, im sure you would rather have had the Elf take the ring to the cracks of doom, im just trying to stop you making more people misunderstand frodo.
Frodo & Sam are the biggest, most important characters in the whole story, book or film, the others do important work but at the end of the day its Frodo who takes the Ring to be destroyed and its Frodo who saved the world.