"On" is correct. In the United States, the word "my" is usually unnecessary and would usually be left out. The following examples are correct:
"I will be on vacation from May 30th through June 2nd."
"I took this picture while I was on vacation last year."
"This is an automated message. I am currently on vacation. If you need urgent help, please contact my assistant, Ruth Adams."
Here are some other examples of prepositions used with certain words.
"This year I'm going on a trip."
"The Boy Scouts went on a hike."
"Those news articles make me afraid to get on a plane."
"I've only seen the Northern Lights once in my life."
"In my experience, it is better to take Route 128 even though it is a few miles longer."
"In the 1960s, a manned spacecraft landed on the moon."