NH4+ exists. It's ammonium (not ammonia), so jennielynn_1980 got its name right.
I don't really get this reaction though. A cation + an acid?? There must be something else that's part of the ammonium or...
NH3 + HIO3 makes more sense to me.
How about:
NH3 + HIO3 --> NH4IO3
The product is ammonium iodate. In this case both Alberto_Kravina and geodome are right.
Were you given this equation as you showed us, jennielynn_1980?
By the way, balancing the equation I gave you is wicked easy.