What's the meaning of the phrase 'Toodle-pip'?
A colloquial version of 'goodbye', now rather archaic.
What's the origin of the phrase 'Toodle-pip'?
The British term 'toodle-pip' is a combination of toodle-oo and 'pip-pip - which all mean the same thing. There are several variants of combinations of these expressions 'tootle-oo', 'toodle-doo', 'tootle-pip' and so on.
All of these expressions are considered archetypally English, although you would be hard pressed to find anyone in England now using them. Toodle-oo and pip-pip were the preserve of a certain upper-class English parlance from the 1920s and 30s - more to be found between the covers of Jeeves and Biggles books than in real life.
It would be reasonable to assume that toodle-pip is of the same vintage. In fact it is much more recent - a harking back to the age of country house weekends rather than a phrase actually used then.
The earliest uses of 'toodle-pip' in print come not from England but Canada and Australia. The earliest I know of is in a letter written by a resident of Vancouver, Canada in the newspaper The Leader Post, June 1935:
It's an old southern custom to never stay too long, so toodle-pip.
By southern I assume the writer meant southern Canada.