A qualifier precedes an adjective or adverb, modifying it by increasing or decreasing its quality. In that respect, a qualifier is a kind of adverb (since it always modifies something other than a noun). However, it is not a true adverb, but a structure class word.
How do we know qualifiers aren’t true adverbs? When we check them against the adverb proofs, we can see they don’t pass any of the tests. They can’t be made comparative or superlative, they don’t fit the frame sentence, and so on. Furthermore, unlike most adverbs, qualifiers never modify verbs.
Qualifiers are words like very, quite, too, almost, even, a bit, kind of (see a longer list on page 114 in your text).
Your answer is correct.
Your answer is almost correct. ß Qualifier at work!
It’s cold today. (Mild statement about the weather.)
It’s too cold today. (Qualifier – too cold! We’ll die!)