I'm not familiar with Acid Missile, but my instinct is to say come back when you're level 6+ with a full party and tell us if Zombie is still OP. (It might be, I'm not saying that rhetorically.)
Being "OP" at level 1 is definitely meaningless.
Downsides of Zombie:
--Not being able to take advantage of conventional readily-available healing from potions, scrolls, and casters [Esp. the potions, which are far more commonplace than poison*]
--You can heal many different ways in a round, how many times in a round can you heal
--Your party now has to maintain healers AND poisoners
--All healing will be HoT...can you stack poison?
--HoT and not instant...not ideal when you are at death's door
--AoE poisoning your companions in order to heal might not be the best plan

--Healing essentially always works; Poison can fail...Unless poison always succeeds on Zombies?
--Being disincentivized from taking Body Building, as well as the more minor inconvenience of having to exclude Poison Resist equipment.
* Although if 1/4 of your characters are Zombies, this means 25% more healing potions for everyone else.
The only way I see that working as an exploit is if
all your characters** take Zombie, never take Body Building or Poison resist equipment, and use extra ability points on Poison skills. Which would also mean they can sell all the healing things they find for a little bit of extra gold.
** Or all your characters that will be clustered together, i.e. all your melee or all your ranged characters are zombies and all poison themselves together at a safe distance from the other party members.