With this configuration (hardware+software), the LED was blinking at 1 time/second but the blink pattern was not my expectation. The LED is Off when the clock is updated and it is On at 0.5 second later. Quoted from the Control Register section of the DS1307's Datasheet:
I want the reverse pattern (the LED is On when the time is updated and it is Off at 0.5 second later). So, I will add an invert logic before the LED like:
I have a plan to use this square wave output of the DS1307 for generating an interrupt to instruct the MCU to read time from the DS1307 and I will keep in mind that "The clock is updated at the falling edge of the square wave". The complete clock will be posted here later.