Totally off-the-cuff guess would be that an "ak" word ending in English does not always signal a short-a, hard-k pronunciation. Of course, a quick scan of /usr/dict/words shows me nothing else that ends in ak, without being a proper noun or having a preceeding vowel like e or o, except for "flak." Since the latter was an abbreviation (or whatever one calls a shortened version of those nasty German compound nouns) of fleigerabwehrkanone I guess we can throw it out an example case.
This just leaves me with the default "it was a mediocre attempt to translate a name that does not fit well into the phonetic symbol set available in English" answer.
Another possiblity is that because the english version of the full name of the country is "Al Jumhuriyah al Iraqiyah" the first four letters of the short form of the name were used. In other words the q makes more sense if you know that the letter following it in the full name is an "i"
It's because it is transliterated from Arabic.
Here is the word Iraq written in Arabic:
عێراق
(at least according to http://en.wikipedia.org/wiki/Iraq )
The word ends in the letter 'qaf'.
(see http://en.wikipedia.org/wiki/
Ara...Arabic_alphabet )
Stand-alone form of that letter:
ﻕ
I don't know much at all about the subtlties of Arabic, but its alphabet is very similar to the Hebrew alphabet, which I've studied.
The equivalent letter in Hebrew is ק(qoph/quph/qoph/kuf). It is basically the same sound as the English letter 'k'.
It can be transliterated with a 'k' (if you think vocalization is the priority) or normally 'q' (which traces the letter back to its roots.
Rough transmission of this letter through the ages:
Proto-semitic: (circle with vertical line from the top passing through the bottom)
->Hebrew/Arabic/Phoenician/Assyrian
(as described above) (Modern Hebrew: ק )
->Phoenician to early Greek 'koppa' Ϙ, ϕ (the letter between pi and rho)
->Early Greek to latin 'q'
->Latin to English 'q'
Hope that sheds some light...
It should show how good your browser's unicode and right-to-left support is, if nothing else. 
(Wish I knew how to do the goggly-eye smiley you did in a previous post :-P )
and kaf (ﻙ. The former is an "emphatic" (which is to say uvular) consontant whereas the latter is a plain old velar consonant, like 'k' in English, albeit palatalised and unaspirated.
So it's not just because of the transliteration, but because it's really a distinct sound.
Anyway, thanks to everyone who replied.