I know it's not what you're asking for but the first part might also need checking if you haven't already - you're writing in a time before the big fen drainage projects and I don't think there would have been much in the way of good roads out that way. Even if there's a reason they need to go via Lynn, I think it probably would still make more sense to take ship from London itself, and very likely quite a lot faster. (Gut feeling says it would probably also be cheaper, but I have to admit I've got nothing to back that up with.)

Journey time wise, I feel like 5-7 days would be entirely plausible, but could easily be longer if plot reasons call for it, perhaps because of weather, or because the ship is making other stops. (A few years back, my spouse was supposed to sail from Newcastle to the south coast in a 60ft boat, and that was planned to take between a week and 10 days and they were taking it easy.)

In terms of operational life it seems entirely plausible that that ship would still be sailing a few decades later, if she'd been maintained - the reason there are only a small number of hundred-plus-year-old wood boats on the Norfolk Broads has nothing to do with the theoretical working life of the boats themselves (and everything to do with the fact that a great many of them were used as decoys during WW2 and, unsurprisingly, did not survive the experience...)