My dd, just turned 6, was this exact same way (including the reading another book while I'm reading to her crazy ). She read very early, as a whole-word reader, and after a brief interest in the toddler years, refused to spell.

FWIW, dd's kindergarten teacher (at a gifted school) told us that it is very common for early readers to be poor spellers at first. She said learning phonics would help, and it did. DD started the year at a "beginning of 1st grade" spelling level and ended the kindergarten year at "end of 2nd grade" spelling level. Still, no where near her 5th grade reading level, but improving, none the less.

One thing I think really helped was an emphasis in her classroom on "Best Guess Spelling." DD's perfectionist tendencies had made her unwilling to guess. But for certain assignments, the teachers required the class do "best guess spelling" - to be corrected later - and dd learned she had to make some sort of attempt to complete the assignment. I think it took away some of the stigma (in dd's mind) of being "wrong" and made it simply part of the process.