It's a meaningless phrase used to say goodbye. Developed from the equally meaningless phrase "Toodle pip" or "Toodle-oo", which dates to the early 20th century.
See here for more about it: http://www.word-detective.com/111606C.html#toodle
Toodley doodley=?Son: I've got the best dad in the world.
Dad: Now you know how that embarrasses me.
Son: I know. Toodley doodley.
Dear Agony Aunt,
You always can help me out. Thank you very much!
You're not having relationship problems, are you daffodils?