Stowaway to the Mushroom Planet, by Eleanor Cameron, 1956.

I own all the sequels to Wonderful Flight and will probably give them away to my friend after reading them again. They just don't hold up that well, alas. Horatio Q. Peabody, the meddling, egotistical young man who stows away aboard Chuck and David's spaceship, is a funny character, but otherwise the story is not very interesting (aside from the briefly-mentioned, ominous "hole in space"--I hope it shows up again in the later books). There's the same strange feeling that Mr. Bass and his Basidium counterpart, Great Ta, somehow know and control everything that happens. But now that I think of it, it does make David and Chuck's experiences similar to those of a child--that feeling that grown-ups are omniscient and omnipotent.