In Latin, <qu> is a digraph used to represent the labiovelar stop [kʷ]. The spelling entered English via Latin and French. Native words with [kw] used to be spelled <cw>, e.g. cwēn "queen", but <qu> took over. Note that in some cases, English <qu> is pronounced [k] as in Modern French, e.g. antique (and others ending in -que).
The letter <q> is also used in the romanisation of words from other languages.
This is a productive source for new words containing <q> not followed by <u>. Wikipedia has some English examples, but the same holds true for German in principle (but see the last paragraph).
Transliterated Mandarin: qi. The Mandarin pronunciation of <q> apparently is [tɕʰ], for which native speakers of English can substitute [tʃ].
Transliterated Arabic: niqab, where <q> stands for IPA [q], for which English speakers substitute [k].
In short: Words that contain <q> have different sources, and the pronunciation varies accordingly. The observation that <q> is almost always followed by <u> in English is derived from the status of <qu> as a digraph in Latin and the abundance of loan words from Latin and French.
One difference between English and German is that in Old High German, [kw] was always spelled in the Latin manner as <qu> and not <cw> as in Old English. Native [kw] seems rare. In the example of OHG queman, it became [k] (NHG kommen), whereas it was retained as [kv] in quellen, quälen, (er)quicken.
Furthermore, German prefers nativised spellings over transliterations. For instance, where English uses Quran, German has Koran. This can lead to funny juxtapositions such as that between nativised Burka and transliterated Niqab in this news article.