The only solution to maintaining long-term sanity: Strict population control, and strong rituals to hold their tiny culture together.
The dwarves will develop the traditions on their own, with yearly cycle revolving around harvest seasons, and the accompanying bursts of activity. The occasional growth of a tree or bush every few years would warrant vault-wide celebrations. Dwarves would grow up dreaming their whole lives about making the perfect sock to sacrifice to the cinnabar god.
I'm assuming you will do population control manually, but just for fun, I'm also thinking of a more automated solution: A single trapped bedroom designed to kill anyone who tries to enter. Eleven dwarves will survive, but whenever population gets too high someone will claim the twelfth room for themselves and be sacrificed for the good of the vault.
Also, a fun thing that I used to play around with in 40d: When the time comes, seal your fort, and then use some DFHack magic to erase the rest of the map, so that your fortress will forever sit alone on a tiny pillar of rock in the middle of a vast sea of otherworldly nothingness.
The trapped bedroom is a very good idea, I want this to be as autonomous as possible (the still and lever will have to be somewhat manual because the almighty cinnabar god would probably perform too much population control if someone was always pulling the lever as other hapless inhabitants tried putting stuff under it).
Make sure there is one breeding pair with military skills. Or some way to train military skills.
Military Dwarves don't mood. This'll ensure you'll have at least one pair to pick up the vault in the event of Dwarf annihilation.
Also, behavioural sink
Thanks for the military tip - I have a perfect idea for training military skills!
1. Archery range, not sure where to put it but they don't have to be very long, right?
2. Bone bolts produced by the craftsdwarf's workshop.
3.
Twelve Eleven +copper crossbows+ for the inhabitants. If married couples end up occupying the same bunk so we get twenty-two dwarfs, more can be made out of wood.
And the idea of a circle of strange quiet dwarfs (I imagine them as being dressed in all-white and having no social skills) desperately waiting for a tower-cap to burst up through the cavern dirt strikes me as hilarious somehow. Of course, if the parents don't teach their kids every word they know, and the process repeats, eventually they'll make up their own bastardized half-dwarven language, creating a bucket of laughs for whichever poor sod unseals the place five hundred years from now.
"ZMERKY THE BRIDGE GOD OF A JJDSX FIVE!!"
"Oh god! They're insane! Pull the lever!"
"
GAAAAAH WEDIJ MAGMA!!"