Although the Dwarves in Moria died long before The Lord of the Rings: The Fellowship of the Ring, Gimli somehow did not know and actively encouraged the Fellowship to travel through the mines of Moria. 30 years before the beginning of The Lord of the Rings: The Fellowship of the Ring, Balin, one of the dwarves who accompanied Thorin Oakenshield in The Hobbit and Gimli’s cousin, led a mission to reclaim the abandoned Dwarf kingdom of Moria. There, the Dwarves hoped to reestablish their kingdom and even recover a lost Dwarf Ring of Power. While the colony was initially successful, Orcs and Durin’s Bane, the Balrog, attacked them five years later, killing all of the Dwarves.
However, Gimli did not know about the Dwarves’ fate in The Lord of the Rings: The Fellowship of the Ring. Excited to see Balin, Gimli was horrified when the Fellowship entered Moria and found only bones. As they were forced to continue traveling through the caves, the Fellowship of the Ring eventually found Balin’s tomb and the Book of Mazarbul, which recounted the Dwarves’ experiences in Moria and ultimate defeat by the army of Orcs. Soon after, the Fellowship had to fight not only the Orcs, but a Cave-troll and the Balrog, resulting in Gandalf’s death.
This disastrous outcome raises the question of how Gimli did not know about the Dwarves’ failure to hold Moria. Since Balin and his company had not contacted anyone for 25 years, it seems like Gimli should have been more suspicious of entering the underground kingdom. According to one theory (via Stack Exchange), Gimli did not know about the fall of Moria in The Lord of the Rings: The Fellowship of the Ring movie due, effectively, to poor communication. Gimli and the other Dwarves lived in the kingdom of Erebor and, since Erebor was far away from Moria, news would have been slow between the two kingdoms. The journey to Moria was dangerous, so many messengers could have died going to or from there. After enough messengers died, the Dwarven King Dain of Erebor, who had not approved of Balin’s mission to Moria, might have given up and stopped trying to contact Balin.
However, poor communication is not the only fact worth considering: 25 years still seems like a long time to have not heard from people and to assume that they are still alive. However, according to the theory, this timespan might not have been too concerning to Gimli and the other Dwarves as Dwarves can live around 300 years, so their perception of time would be different from that of humans. Combining the poor communication between Erebor and Moria with the Dwarves' extended lifespans, Gimli might not have known about the fall of Moria simply because Erebor had not grown too worried about the lack of information yet.
While, In The Lord of the Rings: The Fellowship of the Ring movie, Gimli had no idea that Balin had died despite having not heard from him in 25 years, this was actually a major change from the books. In J.R.R Tolkien's The Fellowship of the Ring book, Gimli and the other Dwarves knew that something must have gone wrong in Moria. Their concern for Balin was the main reason Erebor sent representatives to the Council of Elrond in Rivendell, where the Fellowship of the Ring was created. Due to this, Gimli did not urge the Fellowship to travel to Moria, viewing it as a last resort. When the Fellowship was forced to enter Moria though, Gimli hoped to learn what had happened to Balin. Unfortunately, the Fellowship’s journey only confirmed what he had feared. Although Gimli knew that Moria could be dangerous in the book, he did not know about Balin’s death in The Lord of the Rings: The Fellowship of the Ring movie possibly due to slow communication and Dwarves’ perception of time.