Rat poison is safe around cats as long as it is not directly accessible to the cat, a cat eating a poisoned rat will have no affect on the cat, modern poisons are not permitted to allow secondary poisoning.
I prefer poisons but if you can catch it in a trap, job done, use peanut butter in the trap so they spend ages licking it off, set the trap as fine as you can!
Of course you can have just one rat, 80% of rat/mouse infestations are caused by cats bringing in a caught rat and dropping it in the kitchen.
There is no such thing as a "Plummer jack russell" unless the Plummer Terrier was crossed with a Jack Russell. and it extremely unlikely that any terrier will catch a rat in a house unless you prepared to take the floors up and take the walls down.