As demonstrated in LoTR where that girl kills that dude, magic is worded very specifically. So if the ring was forged with magic that talked about "any craft that we here possess" then yes the Death Star probably could destroy it, because the magic would not have been created to defend from that type of power.
In fact a standard laser could probably have destroyed it.
If the creation magic was "Only there can it be unmade" then the ring would be quite safe.
Lucky for the One Ring creation was "only there can it be unmade"
However, a friend of mine schooled me on LOTR lore when I posted this thread on my FB. Basically if the planet was destroyed, than that means the Maia and Valur (sp?) would also be destroyed. Hence the Sauron is dead, the ring is now just a gold ring. His soul/power no longer inhabits a portion of the ring. A second shot would take the ring itself. I'll repost that info here in an edit.
EDIT: [My friend Jerry]
i consider myself a Tolkien master and i will have to say that when the world was created in the Silmarillion, it was created by music, making the possibility for a deathstar to be made impossible, due to the lack of nuclear material necessary to power it. but if we where to cross realities, then we have to take in the fact that Ea is a planet while the Deathstar is a planet destoyer, and without the existence of the planet, the Valar would not exist, and if Aule dies, then sauron dies, no matter what. plus, there is no space defence on either Middle-Earth or Aman. thus, Deathstar>One Ring
the ring is a hoarcrux, and it has a spell that makes it indestructible except for the fires in which forged it, for they are the hottest fires in all of Ea. yet the existence of the Maiar is dependent on the existence of the Valar they served and who created them. in the Silmarillion, Eru, the father of the Valar, stated that if Ea should break, then all life would end. if Aule should die, so would Sauron, and the one ring would just be a piece of gold floating around in space. Deathstar>One Ring [/My Friend Jerry]