,the journey will take about an hour and a half and i would like it to be as stress free and as comfortable as possible. i would be grateful for any advice
Check your girth after a couple of hundred or so yards, and walk it most of the way. You might get trot, but don't expect canter. Wear a few pairs of pants so your bum doesn't get sore.
Remember to clip its wings when you get it home
Seriously, though, I would be inclined to transport it in a horse trailer, with all the bars and partitions taken out, with a good bed of shavings down, and the top doors closed. If they are prone to panic, you may wish to put a dark coloured sock over its head till it's loaded and ready to roll. I think Rheas are ok, it's Cassowaries which are flighty and easily shocked.
Watch its feet...they can give a hell of a kick.