Hi there,
Welcome to KL! (Well, almost...!)
International schools here are very used to accepting 'rolling admissions' - i.e. students throughout the school year - so it should be no problem enrolling him in March/April.
You've got Havil International & Global Indian International School both right in Brickfields, and both within your budget.
I would also consider Taylor's International School, which is just a little bit further way, but a very good school indeed for the price. I'd definitely suggest taking a look.
Cheers