lord of the rings - Why didn't Gimli know Moria had fallen?

The references in The Hobbit are from a different "fall of Moria". After the events in The Hobbit, a dwarf named Balin, from the company that traveled with Bilbo, attempted to reclaim Moria once more. In the movie, Balin is the old-looking dwarf with white hair.

His success was short-lived, though, as we find in The Lord of the Rings. Hence the tombstone which reads "Balin, son of Fundin, Lord of Moria".

Both Gimli and Gandalf know of Moria being a dangerous place, but they don't know Balin's mission has failed so catastrophically.

From Wikipedia:

In T.A. 2989 Balin left Erebor and entered Moria with a company of dwarves including Flói, Óin, Ori, Frár, Lóni, and Náli. He discovered Durin's Axe. Balin's colony was overrun by orcs soon afterward, and Balin was killed by an orc archer in the Dimrill Dale in 2994.

In The Fellowship of the Ring, the title characters discover Balin's tomb in the Chamber of Mazarbul. Gandalf finds the dwarves' book of records, and discovers from it that Balin was killed by orcs.

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In addition, I do not think Gandalf knew for certain that Durin's Bane was a Balrog, or that it had been reawakened. In The Mirror of Galadriel, it is at least shown the Elves from Lorien weren't sure themselves, and also Galadriel shows some insight into why Gimli might want to see Moria in spite of the danger. Here's the relevant exchange:

Celeborn says:

“We long have feared that under Caradhras a terror slept. But had I known that the Dwarves had stirred up this evil in Moria again, I would have forbidden you to pass the northern borders, you and all that went with you.”
(FotR, The Mirror of Galadriel. Source: "Celeborn and Galadriel", The Council of Elrond)

To which Galadriel answers:

“If our folk had been exiled long and far from Lothlórien, who of the Galadhrim, even Celeborn the Wise, would pass nigh and would not wish to look upon their ancient home, though it had become an abode of dragons?
Dark is the water of Kheled-zâram, and cold are the springs of Kibil-nâla, and fair were the many-pillared halls of Khazad-dûm in Elder Days before the fall of mighty kings beneath the stone.”