Do I need a dot over each note? Is one dot over one of the notes enough?
Staccato is stem specific rather than head specific. Thus one dot will suffice. The other way would be to make the note actually exactly as long (short!) as you want, then put the appropriate rest. Staccato itself, to me, is a bit vague, and can be interpreted in subtly different ways, as far as note length - brevity - is concerned.