"Would a brain transplant suffer immunorejection if the new body was cloned from the original?"
No, thrice no, definitely no and indubitably no.
"The main problem is immunorejection"
Nope, there's not even the smidgen of a hint of a faint suggestion of a problem of that if you're using a cloned body.
And as it happens theres not as much of a problem with a brain transplant into any old random non-cloned body as you might think as practically all of the immune system avoids going in there .. it's a no go zone for much if not most of our bodies defense systems against foreign objects which is why so many viruses hide in nerve tissues to avoid our bodies defenses .. so if there's anything you can transplant and expect a relatively minimal immune reaction from the body then that's it.
Sure the immune system can attack the brain .. encephalitis is a thing .. but not all of it can effect the brain which will reduce the types of immune suppressant treatments you might need and also allow some elements of the immune system to safely remain active to protect you from infection.
But that aside allow me to suggest a small additional procedure, inject a very small number of pig stem cells into the sole of one foot of the developing embryo of your people, done correctly at the right stage of development it will have no effect on the developing baby except allowing it to accept any and all transplants from a clone of that pig with no immune reaction at any later point in life .. it essentially tricks the developing immune system as it calibrates itself into recognising the pig DNA as its own .. keep your original body healthy longer with any repairs or spare parts it might need.
Which unless you have a way to fast track your clones or you start one for everyone as soon as they're born and everyone always has a spare adult clone on hand is something you may need to keep you going while you wait for your clone to grow enough for your brain to fit in its cranium.
Incidentally, a useful little trick to use if you want to be someone else in your next body that, you can use it to 'inoculate' a new clone of anyone you like against rejecting your tissues, man, woman, even reasonably compatible animals (that provide your brain's nutrient requirements in their blood, who's bodies operate at an appropriate temperature, etc), you can be them all if you want.