RHD isn't a problem. A few teams have already done this, including my team with an MG Metro 1300.
Technically you'll need a waiver from Lemons HQ because of Rule 2.1, which states, in part, that entry is "limited to mass-produced, four-wheeled vehicles legal for U.S. highway use at the time of their manufacture" but HQ has made it clear that they're happy to grant such waivers for anything that was manufactured in compliance with a reasonable set of safety standards somewhere.
I wouldn't worry about shipping costs. The judges would be happy to see something like this.
My biggest concern would be crossing the border with it. If you've got it titled and plated in Canada, this shouldn't be a problem (but check before showing up at the border anyway). If you intend to bring it in without all of that, look very carefully into what Customs will want to see.
Edit: With RHD make sure your drivers put their wristbands on their right wrists instead of their left, as this will make it easier for those of us Lemons staffers who have to check such things each time the car goes on track.
1982 MG Metro 1300: IOE 2015 Pacific Northworst GP, Longest Distance 2010 Cd'L Box Wine Country Classic
1980 KV Mini 1: Worst of Show and Fright Pig Supremo 2009 Concours d'Lemons
1978 H Special: Second-Round Elimination 2010 Lemons Pinewood Derby at Sears Pointless
1967 SAAB 96: IOE 2012 Pacific Northworst GP