Using texinfo.tex version 1999-09-25.10 and the Debian texinfo 4.0 and recent tetex, I noticed that putting the document below through texi2dvi puts the caret over a blank space and the "q" as the next character, unaccented. Other accents like \vec or \widehat work, as does an explicit \mathaccent"705E. Is texinfo.tex redefining \hat? It'd be good if it could work in math mode too.
foo.texi