You should not have to be watering every day unless you soil is extremely fast draining (sand and rock).

Additionally, peat moss is acidic and tends to compact over time..

Fig trees prefer a more alkaline, faster draining soil.

If your temps are in the high 90's and into the 100's, watering every other day should be enough.

If cooler, every third or fourth day might well be enough, but again, this will depend on soil type. You can probe a bit around the base of the tree to determine if it needs water. If the soil is damp, let it go another day.

If it were my tree I would (as carefully as possible) remove as much of the peat moss as I could without disturbing too many roots. I would back fill with native soil mixed with a bit of compost, and then mulch around the base of the tree. You can also add some garden lime to help with soil ph.

It wouldn't hurt to cut the top foot or two off your new tree either. If it's in shock and your roots are under performing due to the peat moss, it is probably not delivering sufficient nutrients up into the tree...hence your leaf drop. With a shorter tree, there will be less tree to feed. Don't worry...a healthy fig tree will put on two to four feet of new growth after it's first year in ground.

What is your soil like in your yard? If it becomes sticky when wet, adheres to your shoes when you walk through it, and dries real hard...mix more compost in and consider planting the tree several inches above ground level and building a mound around the base with a compost soil mix.

Some will disagree with me, but I like to build a moat around the base and fill with water a couple of times a week.
This allows the water to soak in deep. The moat should be at least three feet in diameter for a newly planted tree. After a year or two you can break down the moat or fill it with compost or mulch to help keep the soil cool and moist.

I mulch 4-5 inches thick with straw as a ground cover. It ain't real pretty, but it's effective.

This should give you some ideas. Good luck with your tree.

Dave

The falling off of the leaves is due to excessive rain in your climate this year coupled with excessive watering you gave the tree.
The leaves develop rust and fall off.
Ask people in Southern Florida,they have this problem every year.
Solution:Build a soil mound around tree,and stop watering.
Ideal climate for figs ,have 25 inches of rain or less annually.