Should it be "doxxed/doxxing" or "doxed/doxing"?

The Oxford Style Guide says, for example, that:

When the final consonant is w, x, or y this is not doubled:

tow, towing, towed

vex, vexing, vexed

However, it seems that doxxed/doxxing are more common than doxed/doxing. (When I search on Google, doxxing has 4.82M results while doxing has only 1.48M.)

So which is "correct"? Double x's or single x?

The rule that you quote is about words that end in a single x in the base form. So this rule doesn't even exclude the spellings doxxed and doxxing as inflected forms of a verb spelled doxx (and the double-x spelling is in fact attested for the base form).

In any case, there isn't really a way to determine the "correct" spelling of a word like this. In my answer to “Focussed” or “focused”? Rules for doubling the last consonant when adding -ed, I mentioned another word that you might see spelled with a double xx before -ing or -ed: exxed (as in "exxed out"). As you can see from the answers to that question, the rules of consonant doubling in English spelling have some exceptions, so the fact that a spelling is irregular is not certain proof that it must be considered "incorrect".