The door of durin.

[Rumil]

I think it was indeed a little slip by JRRT.

Not Gandalf's description, because as Galadriel says it could be on-the-spot translation. But the elaborate drawing Tolkien made of the inscription also says Moria, and Khazad-Dum apparently wasn't called Moria until the whole unfortunate Balrog incident.

Hollin and Khazad-Dum seem to be as close as the dwarves and elves ever got, so its logical that the inscription would be in elvish. What we don't know is the elvish for Khazad-Dum before it was called Moria - that's what should be written on the doors.

On the other hand perhaps it always was Moria but with a less dire spin, would something like 'dark caverns' be appropriate?

Meanwhile on the 1st Age feuds, refugees from Nogrod and Belegost moved to Khazad-Dum after the War of Wrath at the start of the Second Age.

Interesting to think that Moria is by far the oldest Middle-Earth settlement that we know of, going right back to the First Age and probably before, so at least 7000 years old. Though there might well be four similar Dwarven strongholds in the East (Yellow and Red Mountains I'd reckon), and maybe Mount Gundabad might count?