Suppose I have a 9/8 time signature and I need to a put a rest somewhere which is worth a dotted crotchet (quarter note). Do I write a crochet (quarter note) rest with a dot or do I write a crochet (quarter note) rest and then a quaver (eighth note) rest separately?
It's the same thing. Dotted notes can be used in any time signature. The dotted crotchet signifies that the rest is for a crotchet and a quaver. If it fits the measure, it can be used, like in your example:
But you can also use two rests, a crotchet and a quaver:
If the grouping is 3-3-3 (quavers), I think the former case is more likely to appear.
There is a school of thought that forbids dotted rests entirely. But I think the rule may be broken when the dotted rest comprises a complete beat (and starts on a beat). Go with the dotted rest.
It somewhat depends on the location of the rest. If the 9/8 is meant to be a threefold division of three beats, then the dotted quarter rest should only be used on beats 1, 4, or 7. If the division is (the rare) 4+4+1 eighth notes, then the dotted rest should only appear on beats 1 or 5. Similarly, a quarter rest probably ought not to start on beat 2 (unless the underlying division is 1+4+4 eighths but that is difficult to distinguish form 4+4+1.)
I personally never (rarely anyway) use dotted rests; I just find dotted rests harder to read.