An Overview of Khuzdul
In The Lord of the Rings, we actually learn very little about Khuzdul as a whole. There are some example words which are mostly place-names. There are a few details about phonology and writing, but little else. All else we find out is that the Dwarves "used their own strange tongue, changed little by the years; for it had become a tongue of lore rather than a cradle-speech, and they tended it and guarded it as a treasure of the past." The Lord of the Rings, Appendix F.
To get a broad view of Khuzdul, we have to turn to several sources. These include The Silmarillion, various volumes of The History of Middle-earth Series, The Letters of J.R.R. Tolkien, and others. The following is a list of quotes describing Khuzdul.
The first five references describe Khuzdul as being a tongue that had a harsh sound to it; one which the Elves found unappealing. Additionally, it was intricate and complicated, and thus difficult to learn.
The last two references are more interesting. The quote from Sauron Defeated references "Khazadian", which is actually Khuzdul, and "Avallonian", which refers to Quenya. Because it says Adunaic resembles Khuzdul most where it is different from Quenya, that means that we can compare Adunaic and Quenya, find where they differ, and thus have at least some suggestion that those features may be similar or identical in Khuzdul. There is a good amount of information about Adunaic to be found in Sauron Defeated, so this provides a chance at learning about Khuzdul in an indirect manner.
Lastly, Tolkien himself tells us that Khuzdul's phonology resembles Hebrew, and the noun inflections have at least some comparison to Arabic. What varieties of Hebrew and Arabic he meant, it's impossible to say, but it may just be a general similarity. Modern Hebrew and Modern Standard Arabic were present in Tolkien's lifetime, so we can look at those, as well as older languages like Biblical Hebrew and Classical or Koranic Arabic for comparison. It's worth noting that these are the only real-world languages to which Tolkien refers when speaking of Khuzdul, so these should serve as primary sources for inspiration in expanding Khuzdul.
Interestingly, a language that resembles Hebrew phonology and Arabic noun inflection would match up well with the other information about Khuzdul. Hebrew and other Semitic languages are heavy on "gutterals", which are consonants pronounced in the back of the mouth or in the throat. This could be interpreted as "harsh" or "unlovely" sounds, depending on the listener's perspective. Arabic is widely known as being difficult to learn, largely as a result of it's "broken plurals" and syntax. The verbal system found in Hebrew is also regarded as being difficult. Add those together and, truly, you have a language that is "intricate" and "complicated"! Sounds perfect for an expanded Khuzdul.