Tracey,
Haddonis are about the least picky of the host anemones regarding light. If you can keep LPS under the lights then you can keep a haddoni.
However, with the fish you have in your tank, I would think twice about adding a haddoni carpet. They are notorious fish eaters, especially of tangs and dwarf angels. There will be some people who say they have had no problems, but its like playing with a loaded gun. Keeping clowns with the anemone won't help and neither will keeping on a night light. It looks like you have some nice fish there. I would hate for you to lose any just because you didn't know.