"Avada Kedavra" never actually destroyed a Horcrux. There was Basilisk venom, Fiendfyre, Gryffindor's Sword... and the twin cores of Voldemort's and Harry's wands fighting each other.
The ring was made with the lava in Mount Doom. Therefore it would make sense that only the lava in Mount Doom could unmake it. Also, the scene where Gollum dives in after the ring is in slow motion, it doesn't really take THAT LONG for Gollum to sink. Neither did it take long for the Ring - it goes in, tries to fight the lava [the lava starts to harden around the Ring, getting darker] and then the Ring sinks.
Are there basilisks in LotR? Not in the movies.
Basilisk fang does not equal doom for the Ring.