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The 33-year-old personal trainer from Devon, England, has been running up to 60km a day, pushing a ''cart'' filled with up to 30kg of food, clothes, a tent and sleeping bag.
Unfortunately, the cart looks like a pram, which has alarmed the public and police.
''I've had lots of police stop me because people keep complaining about a man pushing a baby buggy alongside busy roads.''
While it had been awkward explaining his situation to police officers - particularly those speaking foreign languages - it was usually resolved when they found no baby in the cart.
To date, Mr Carr has run 15,000km across England, France, Belgium, the Netherlands, Germany, Denmark, Sweden, Finland, Estonia, Latvia, Lithuania, Belarus, Ukraine, Romania, Bulgaria, Turkey, India and Australia - all with the aim of raising funds for Red Cross and the mental health charity Sane, and setting the world record.
He has gone through seven pairs of shoes - two of them to cross Australia.
His run started at Hay Tor, in Dartmoor, England, in July last year, and he hopes to run more than 29,000km, west to east, over six continents before September next year.
Jesper Olsen, of Denmark, was the first to attempt the record in 2007, but did not qualify because his run was 2000 miles (about 3200km) short of the prerequisite distance for the Guinness record.
He did it in 22 months.
Australian Tom Denniss did it in 20 months and 13 days but was also short of the distance required.
''I should do it faster than Jesper but it would be very unrealistic to break Tom's record.
''Guinness don't recognise their runs because they both did about 16,000 miles [about 25,700km], but Guinness state you have to do 18,000 miles [about 29,000km] to be recognised.
''I'll get it by default, because I'll be running that extra 2000 miles.''
Mr Carr started his New Zealand leg of the run in Queenstown on June 7, and arrived in Dunedin at the weekend, just in time to see his beloved England play the All Blacks at Forsyth Barr Stadium.
While he was physically coping well with the journey so far, he said travelling from India and Australia, where temperatures reached 42degC in the shade, to New Zealand where temperatures had dropped to as low as -6degC, had been hard on his body.
''Basically, I haven't been below 25degC for four and-a-half months. And then my first day in Queenstown, the temperature was 4degC, -2degC with wind chill.
''My tendons were not liking it at all.
''It made me feel pretty sick, but I've got used to it now.''
Mr Carr camps out in the wild most nights and sleeping among snakes, spiders, scorpions, bears and dingoes has been relatively comfortable.
''If you spend all night worrying about it, you lose sleep and then you'll probably get run over by a road train, because you're too drowsy to notice it coming.
''That's more realistic than being bitten to death by a snake.''
Mr Carr left Dunedin yesterday afternoon and hoped to reach Auckland within the next month.
He will then run through North and South America and ultimately back to his starting point in England.