A necropsy by a vet would have a good chance of determining the cause of death. Given how effective this knowledge is in avoiding future similar problems, the cost (about $150 +/- for gross necropsy, plus any pathogen tests, cytology, etc) is a very good value -- a sort of investment in one's own knowledge and care practices.
While I don't know which pathogens are transmissible between the animals you keep, since it is possible that the beardie had a detectable pathogen that didn't contribute to its death (e.g. there were symptoms but not ones you noticed and not ones that played in role in the death), the necropsy may be valuable in that regard. Whenever a pathogen is suspected, getting it tested is good practice.
"Rescued" (this covers a range of situations) animals should probably get an initial vet check regardless of apparent health status, since they are generally less well cared for than animals acquired in some other way (directly from a quality breeder, or from a keeper who is relinquishing a well cared for animal for other reasons).
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