If Gimli was the Ring Bearer

If Gimli was the ring bearer there would be a bunch more elves and dwarves going and no hobbits! Gimli would have no Sam. Legolas would not become his sam because Legolas would have lots of elf buddies to keep him company and he would not succumb to that level.
Aragorn, Boromir, and Gandalf would still go because they are heroes and they need to go on an epic journey before their life ends. And Gandalf has to turn white. Boromir has to die, and Aragorn needs to work through his recluse attitude and become a king. If Gimli was the ring bearer then the journey would be slower than if a hobbit was the ring bearer. For dwarves eat more and slower, and aren't good on endurance, so the fellowship would travel at a steady dwarf walk.
The Fellowship wouldn't step foot on Caradhras because the dwarves would put their foot down and start walking to the mines of Moria alone. But Boromir would of course ask Gimli if he would like him to carry the ring over the mountains and meet him on the other side. That would not fly very high. When entering into Moria the dwarves would see that their entire race is dead and the fellowship would safely exit the mines because no one is stupid enough to wake the Watcher.
After the Mines of Moria incident the elves would take charge of navigation and bring the fellowship to Lothlorien. Where Galadriel would reprimand Gandalf for not fighting the Balrog and turning into the white. She would then reveal to the fellowship that the mission was beyond hopeless because Gandalf the Grey is essentially useless. Boromir would then ask Gimli if he would like him to take the ring from here.
After the discouraging remarks the other dwarves would realize there really is no gold at the end of their journey and decide to return and the other elves would decide to stay with Galadriel. The company would then be Aragorn, Boromir, Legolas, Gandalf and Gimli.
As the fellowship would make their way across Emyn Muil they discover Gollum following them. Boromir would then ask Gimli if he wants to make a decoy plan and give the ring to him while Gollum still thinks Gimli has it, Gimli will again refuse. one night Legolas would shoot Gollum, and in the morning legolas would be reprimanded for killing the creature that could help in the end.
One day the fellowship would meet Faramir and Boromir would ask one last time for the ring and Gimli would refuse. Boromir then quits the fellowship and defends Osgiliath while Faramir would take his place. The next day as the new constructed fellowship waits on Legolas to capture and kill five Easterlings. They then impersonate the five dead Easterlings and enter Mordor. But that night Gandalf would be found out because his bushy beard, gray sheets, and staff were unable to be hid. And Legolas just looked to unhealthy so they released him without noticing the blonde tips barley showing under the head gear. Gimli would also be discovered because of his height, ergo the ring would be discovered and brought to Sauron. Unfortunately Aragorn and Faramir go unnoticed and spend the rest of their days being servants to the evil lord, Sauron!