This is an interesting bit of history about Pakistan. That Pakistan actually had a queen for a few years. This was Queen Elizabeth II.

Pakistan gained its independence in 1947 from British India. Pakistan was initially the Dominion of Pakistan with King George as its monarch. King George died in 1952 and was succeeded by his daughter, Queen Elizabeth.

Elizabeth II, the reigning queen of the United Kingdom and other Commonwealth nations, was the queen of Pakistan for four years. Yes, the world’s first "Islamic Republic" was ruled by English heads of state for nine years: Elizabeth and her father, George VI. Elizabeth’s reign over Pakistan ended 60 years ago, when, on March 23, 1956, Pakistan became a republic.

India too had initially been a Dominion of the Commonwealth nations. However, it became a republic earlier than Pakistan, so Queen Elizabeth was never the monarch of India.