Minimize Deterministic Finite Automata with no accepting states
A finite automaton without end states denotes the language L = $ \emptyset $ . To minimize a DFA we minimize the number of states and the denoted language must be the same. By definition of DFA we must have an initial state $ q_0$ so $| Q | \geq  1$ and as you say we need to include the transition function with all transition into $ q_0 $ (because creating dead states is counterproductive).