Ae85 swap 4age.

[banpei]

It has been done before and we even had a forum member who simply swapped a 4A-GE head on to a 3A-U bottom, making it a 1.5 litre 3A-GE. But that was a lot of effort for little gain.
The procedure should be mostly the same as for the SR5 to GT-S swap (4A-C to 4A-GE) as described by Assassin10000, with the difference that the AE85 has a K50 gearbox instead of a T50 gearbox. The SR5 has the T50, but is clutch operated instead of hydraulic, hence you need the 4A-GE bellhousing.
Your rear axle is also a different axle (S302/S312/S314) than the AE86 (most of them are T283). You can keep the S axle, but it's harder to find a LSD for it. If you can live with an open diff it shouldn't be an issue.