Well, going based on English pronounciation rules:
"Qu" forms the "k" sound "Kuh" as in "Kuh-een" (queen) or "Kuh-aye-zar" (quasar).
"Que" forms the sound "Kuh-e" (e as in heck) as in "Kuh-e-shun" (question) or "Kuh-e-bec" (quebec)
So, "Queatrix", might sound like "Kuh-e-aye-trix", But like many latin-based languages, English often allows consecutive vowels to be slurred with pseudo-consonants to aid the mouth. Particularly in the case of consecutive vowels, closing or pursing the lips after forming the first vowel aids in forming the next one, as in the conjunction of "Qu" and a vowel. Pursing the lips after sounding "kuh" and then re-opening them to form the next vowel produces the pseudo-consonant "w" (the sound made by blowing air through pursed lips) as in "Kuh-ween" or "Kuh-way-zar". So a more "mouth-friendly" pronounciation might be "kuh-weh-aye-trix". However, the sound "kuh" and its following vowel may be further slurred to form the consonant pair "kw" followed by the vowel. In the case of an "e" (as in heck), it will form the sound "kweh" as in "kwehst" (quest) or "kwehs(c)hun" (question) or "kwehlm" (quelm) (in the case of a, it would be "kway" as in "kwayzar" or "kwayke" (quake)). So now the sound "kuh-weh-aye-trix" becomes "kweh-aye-trix". From here, the "aye" sound may subjugated into the "kweh" sound to produce the final pronounciation as:


However, other pronounciations may be formed depending on how that last step is carried out:

Thankfully, Dave's is a lot easier :
maybe even Sin-Kuh-la