Congrats on making the leap and getting a rabbit! The only rabbits I've flushed this year have been in grouse or woodcock cover. Not much time to shoot with a young unsteady cocker in hot pursuit. So far I haven't even shouldered the gun on one. Woodcock closed here on Christmas Day. Just in time for the hard freeze up north to send the last holdouts moving south.
One pierced primer from just a handful of shots is a pretty high failure rate. You've laid out the options: try shooting some more--with the same or different shells--and see if the one failure was a random abberation or get it to a pro right away for a check up. I tend to send guns in for inspection shortly after receiving them--I've made a couple expensive mistakes by not doing so. I don't know that you'd run a terrible risk in shooting it a bit, but if there were any more indication that something was off, I'd pack it off to someone who knows hammer doubles.
