An early simpson’s quote that has spawned a meme. The original meme refers to a cheese doodle that is being used to bait fish. Ned Flanders offers a “Godspeed little doodle” prayer to the cheese doodle before Homer Simpson fumbles the fish catch.
Meaning good luck, go for it.
Also can imply the person feels you may not succeed, but wishes you the best nonetheless.
An alternate version of the phrase “Break a leg”
“She told me she got back with her ex, and all I could think of to say was Godspeed little doodle!”