I felt the exact same way about Q after the first episode both as a character and as a concept for the show. They basically introduced God in the first episode of a science fiction show and he is annoying and arrogant.
But he is actually one of the best characters by the time the show is over and his all-powerful nature is toned down a little bit.
Season 1 is pretty goofy and inconsistent overall. Give it a chance and accept it for what it is and by season 4 the writing is some of the best in science fiction TV.