I've excavated and studied faunal remains from those period sites in Jordan and Israel for some years. I would expect, beyond Ovis/Capra, to find Bos remains and a small number of Gazella and Dama bones. Also, likely a small amount of Sus. There may be a few wild birds (chukar partridge for instance), tortoise, hare and even (saltwater, traded) fish. The Tal al-'Umayri report (volume 5) and/or the Madaba report (vol 13?) both have excellent faunal reports in them, at least in terms of comprehensive species lists. There are other papers of relevance, of course, that you might consult before heading out.

This reply is probably too late to be of help/interest but the one example of fauna that frequently appears is the ostrich, or at least their eggshells, this is a particular interest of mine because I lost count of how many times while working in Jordan I tried to convince the site director that these were not evidence of trade links with Africa since formerly these inhabited Jordan and on many sites could have been collected fairly locally.  I would be interested to know whether your latest season found any ostrich egg shells and whether they are still being erroneously interpreted a evidence of long distance trade.

We did not find any evidence of ostrich eggs, but that is a very interesting discussion. 

That's interesting, are you at liberty to say where the site was and what its nature was?

KMAP/TNAP (it has switched designation since I was involved). I can go so far as to say it was a tell site, which we have excavated into the Iron Age strata, past that I think you'd have to wait for further excavation/publication.