St. John, NB to Gaspe?

The shortest route is from Saint John (not St. John) via Rte 7 to Oromocto, Rte 2 to St. Leonard, Rte 17 to Campbellton. Rte 2 is divided highway, Rte 7 is a major 2/3-lane highway, Rte 17 is a secondary roadway - paved 2 lane.

I hope you're going to spend some time in NB other than along these highways. The St. John River (yes, St for the river LOL!) is beautiful and the tertiary routes along both sides (Rtes 102, 845, 705, etc) are recommended if you have a smaller vehicle for touring. All these roadways are accessible via motorhome or large trailer but would be more comfortable in a smaller vehicle.

Other options for Saint John to Campbellton: 2) Rte 7 to Oromocto, Rte 8 to Miramichi, the 8 or 11 to Campbellton; 3) Rte 1 from Saint John to Petitcodiac, Rte 2 to Moncton then either Rte 126 or Rte 11 to Miramichi then as per 2.

PM me if you need more details. I live just outside of Saint John.

Have you done the Hopewell Rocks thing? It's east of St. John, and worth a slight detour.
To answer your question, I believe 17 should be fine, IIRC, we've used it a couple of times, and 7 is probably OK, too. In a 20' Roadtrek, though, but I don't recall any places where a larger coach might have had trouble.
If you do hit Hopewell Cape, you could then head north to Moncton, and then use 11 north towards Campbellton/Gaspe. Do the 132 loop around the Gaspe, then return along 17 to 2 to Woodstock/Houlton and exit New Brunswick into Maine.
Sort of a loop tour of New Brunswick and Gaspe.

Just remembered, if you get into Campbellton, NB anywhere near the bridge at Subway St. that crosses into Gaspe, there's a tunnel under the railroad tracks on Subway St. on the NB side, that has a height restriction. I think it's around 10'10". BEWARE. There are other roads that get around it in town.