Church didn't work out. I am going tomorrow so here I am again.
Now at this point, the output of the uppermost flip-flop is 1 and the lower flip-flop is 0 so the counter has counted to 01 (binary 1). OK? The upper x-or gate has a 11 on its inputs (output 0), and the AND gate has a 11 on its inputs so the lower x-or gate has 01 on its inputs (output 1). The next clock causes the lower flip-flop to go to one and the upper to go to zero (10 or binary 2). The counter has now counted to 2.
The next clock causes the flip flops to go to 11 (binary three) and the next clock will cause the flip-flop to go back to 00 (binary 0). So with each clock, the counter goes from 00 to 01 to 10 to 11 to 00, etc or 0,1,2,3,0,1,2,3... that is why it is called a counter.
Look at this circuit and make sure you understand it, because that understanding is basic to solving your problem!
Now that I have you to base one, your assignment is to add gates so that 00 causes the flip flops to go to 01 whenever the output goes to 00 by using the presets and resets. However, once you solve this problem, you will notice that 00 appears on the output for an instant. This according to your original problem description is unacceptable. So you need to fix it. How? (suggestion add more flip-flops... Where?) Think, I am not going to solve this problem for you. Write some things down on paper and share them with me. Use the circuit I pointed out to you on the web as a starting point.