As someone who has fitted 16 valve 4AGE’s into an AE82 and an AE86, do bear in mind it isn’t simply a matter of swapping the engines along with a few extra components. There are very many differences, especially with wiring looms, fuel systems and don’t forget suspension and brakes etc.
If you are paying someone to do it, it will cost an absolute packet.
Depending on what model Corolla you have, if there is a 4AGE equipped model in the same model range, think VERY seriously about finding one with a rough body and swapping EVERYTHING across. It will be far cheaper for you, and mechanically not too hard to do yourself.
Its also a lot of fun