Hardy-Weinburg equation, textbook wrong?

Your mistake is that 0.01 is not q; it's q^2. q represents the proportion of alleles, meaning double the number of zygotes plus the number of heterozygotes. You don't know how many of the red eyed flies are heterozygous, so you can't figure out q directly. You DO know q^2, though, because all white eyed flies are zygous. The rest follows easily.