Would moving a dwarf’s bedroom give it an unhappy thought

Dwarves will generally sleep wherever they see fit unless they have an assigned bed, in which case they will prefer this one. Sleeping in an assigned bed does give happy thoughts, being unable to makes a dwarf unhappy.

However, you don't generally have to bother with assigning beds since dwarves will claim unassigned bedrooms for themselves automatically.

Just a side-note: married dwarves and children share beds.

In the current DF2010 build, the only important things are a bed, to make it a bedroom, and a cabinet, because that's the only storage your dwarves will currently use, so reducing the amount of junk left around as they randomly discard their clothing (junk that can't be cleaned up by any means short of a magma scrub or atom smashing, because it's still marked as owned).

Any additional non-movement-blocking furniture is fine for bringing up the room value (and therefore the happiness it grants); I like chests, bags (it's easier to get high-value bags than most other furniture), weapon racks and armor stands. Even a movement-blocking furniture item, like a statue, is okay if you put it behind the bed (and designate the bedroom before you have it moved in, so you get the full value of all your walls).