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I have a full sized '61 Merc with a 352 two bbl auto, and the engine is probably up to the task, if in good condition. My car had 48k on it when I bought it and the cylinder compression ranged from (as I recall) about 140 up to 155 or 6, for the purposes of comparison. I personally would check the compression and change the oil a few times before going on the trip.
Original (unrestored) cars often have problems with sediments in the tank and fuel system, so if that hasn't been addressed, I would also check the system out and - as Mike said, bring some fuel filters.
I remember going from Nebraska to California in 1964 in our family's '61 Dodge Pioneer wagon, and it created memories for a life time. YOU'LL HAVE A BLAST!