When dealing with queued connection Qt will indeed do copies, however you should always code to minimise copies anyway.
On the small things that you should also take into account you should avoid calling the same methods several times. For example in appendRow you call listOfEntries.size() three times where two would be enough.
Another thing that may help: optimise your views to to only show what make sense e.g. only what is visible on screen or have a fixed number of entries visible at any time. This will lower the number of queries done to your models.