I've seen some enormous Labradoodles, huge.
I would recommend taking a step back, away from the Doodle craze, and looking at other breeds as well. Including Standard Poodles if shedding is your concern.
Finding well bred Doodles that haven't come from horrendous puppy farms, backyard breeders with no health tests and insane temperaments is an absolute minefield. The majority do NOT come from a good background.
Running a 5kg with a dog can be a bit of a pipedream, it will be at least 1-2 years before a puppy is mature enough to do that anyway and even then some dogs don't want to run constantly, they want to stop and sniff, to wee on that tree, sniffing is very important, almost more important than the walking.
If you look at Canicross - that's like competitive running with dogs - there's not many Labradors, Spaniels or Doodles, rather pointer types like Weimeraner and Vizla or even a special Canicross developed breed, the "Greyster" which is a cross between a Greyhound and German Shorthaired Pointer.
Take off the rose-tinted Doodle specs for a moment ;)