4x4x1 should be ok for a avocado tree. If you have 8ft lumbers do that. If you have 10 ft lumber go for 5x5x1.
Use a heavy soil like decomposed granite if you can get it. Or a sandy loam. Don't use bags of compost or potting soil from the store, there's too much organic matter in it that will hold excessive moisture and rot your roots.
that sounds like it would dry out very fast.
in areas where there is high heat/sun exposure, it would dry faster.
in my raised beds i use about %25 sand (when i can), %25 compost, and the rest local soil
(which is a very fine sandy loam)
it works great. the compost dries fast enough,
to not cause a problem rotting papaya or anything else
i guess it depends on how tall the bed is, and how often you want to water.
With a tall bed, it could take years for roots to reach deep enough
i have a CORG thats about 14 inches above grade
i have had to mulch the heck out of it,
and still have to water in dry spells over a week in summer...