Would I be correct in claiming that it is a bit presumptuous that the targ is on the table? I believe It is not typical for targs to be on the table (As they are typically larger than most dogs, and dogs do not belong on tables), and we have not seen targs on any tables. -Daq does not connotate on, but merely gives the location?
While I would probably reject the targ lies at the location of the table as being unnatural English, any preposition that expresses a similar thought would be okay. If you want to be sure that the listener interprets the targ as being on the table as opposed to being at it, say raS yorDaq Qot targh.