Interesting idea, except cattle panels I have have holes so large a bobcat could slip through it pretty easy. Perhaps horse panels instead? Holes on those are much smaller.......some panels as small as 2" x 4" or even smaller. Those are the most expensive you will find on the lot. Not sure you need to use livestock panels, however. I would think 1" x 2" 14 gauge welded wire would be more than adequate......and you can use J clips on that.
How large is this going to be and how do you plan to rig the gate so it will snap closed? What trigger?
As for the livestock panel clips and hog rings.....I'm not familar with anything that large. Much easier and just as secure is light wire typically thought of and described as baling wire. You can get something similar at most hardware stores and most home improvement box stores. A 4" roll of uncoated wire intended to be used to tie concrete rebar together.....simply described as "rebar wire".
To assemble, cut a piece of wire about 8" long. Then bend it double so length is now 4". Then bend that into a 90* angle....loop around both legs of the panels, pull ends together and give it a couple twists. Nothing short of a bear could tear that apart.
Whatever you use, please post some pictures. Curious to see what you come up with.