i am also thinking that in the same way... and one more doubt about alphabet, is it binary or decimal.
for confirmation i asked sample input.
Since it is given that the minimal DFA outputs $1$ $\implies$ we have to make a minimal DFA and then convert it into mealy/ moore machine by associating output with each input or state.
the minimal DFA will be as shown below :-
I am associating output with each input i.e. creating a mealy machine. It will print 1 each time the number of 1's in the input sequence is a multiple of 3.