IMHO you absolutly should clean immediatly after killing. Number one is food safety and meat quality, get the bacteria ridden innards out ASAP and get the carcase down in that ~34F - 40F range quick. Number two it is much easier to clean right away, and if you have ever gutted a deer that was left overnight you will appeciate how unpleasent it is to delay cleaning.
Processsing a couple birds is not a big deal.
-Hold upside down in something (large jug with bottom cut out or bag with opening cut for neck)
-slit the jugulars and bleed out
-Pluck if you want, scalding with hot water does make that easier
-remove all innards, oil gland from tail, feet head ect.
-clean up and wash off in kitchen sink and let stand in the fridge 2-3 days
-cook nice and slow with lots of moisture
If you want to save a bunch of time then skin rather than pluck, should not take more than 15 min coop to kitchen.
Really short on time just kill and slice off the breasts and legs, no need to get into plucking or gutting. But some meat and soup stock is wasted.