Is ill-qualified even a term?

I looked at Merriam-Webster, Oxford, and even Merriam-Webster's Unabridged Dictionary. "Ill-qualified" is not a word offered in any of these dictionaries. However, the use of a hyphen connects the two words and makes a new adjective with a combined meaning, like "just-shined Chevy" or "My I-literally-just-cleaned-him dog went in the mud again," so "ill-qualified" is actually a grammatically acceptable term and able to be used in this regard. Often, these word combinations (for example, "calculus-wise") are in large quantities, and dictionaries can not account for them all.