OK, to start with, Queen Elizabeth died in 1603, however, if you meant the reigning monarch of the United Kingdom, Queen Elizabeth the second, then the issue becomes a little tricky.
QE11, is the world's oldest monarch, but she's not necessarily considered a leader, she is head of state but due to her not having to much legal power, it's a bit of a stretch to call her a leader.
The worlds oldest true politicical leader has recently been sworn in as Prime Minister of Malaysia next week.
Dr Mahathir Mohamad is now 92 years of age! This will be his second term as Prime Minister, after previously serving between 1981 and 2003.
Hope this helps :-)