At first sight, 'toodle-pip' seems the sort of word that P G Wodehouse, for example, might have been using back in the 1920s. However, there is no written record of it anywhere prior to the late 70s. 'Tootle-pip' appeared in 1977 and 'toodle-pip' not until 1983. The latter was a headline in the Standard, so that may very well be where the word originated.
It may signify the sound of a trumpet fanfare marking the leaving of an honoured guest. Another one is Ta-ra! However shaneystar2's version looks good.
According to The Oxford English Dictionary, the origin of 'toodle-oo' is (quote) "unknown", so obviously the scholars there were not convinced about the French origin. However, the sound is so close to it that Shaney's idea certainly seems convincing. I'm afraid we're going to leave the 'jury out' on that one, though.