Here's what we know:
* Doodle is born with a disability: He is described as "a caul around his head" and his brother, the narrator, says "he was not like other babies."
* Doodle's learning to walk is a gradual process: The narrator teaches him by making him "walk" on his knees, then by holding him upright, and eventually by encouraging him to walk on his own.
* Doodle's progress is described as a "miracle": The narrator's astonishment at Doodle's progress suggests it was a long and challenging process.
* Doodle eventually walks: The narrator describes Doodle walking "like a little old man, very slowly and carefully."
Based on these details, it's likely that Doodle's learning to walk took several months, if not longer. The story emphasizes the arduous nature of the process and the gradual progress Doodle makes.
The exact timeframe is not crucial to the story's themes, which center on brotherly love, pride, and the dangers of pushing someone beyond their limits.