I think you can. Use some Vitamin B1 when you move the plant. Figs are pretty tough and if it thinks it's in trouble, it will put it's energy into the fruit. I doubt you will lose the fruit, but the plant could show signs of shock, so keep it in the shade then partial shade prior to putting it in full sun. Good luck!

You shouldn't let a newly rooted fig cutting carry fruit Instead, it should be concentrating all of its energy into becoming an established plant. Once it does that, then you can let it carry fruit.

Rayrose is right

THank you all for your advice. I will move it and disbud the fruits.

3 Gallon pot is large enough for a first year growth of a rooted fig cutting.
Just give it some limestone powder,mixed with mulch in top of container and let it grow.
You can leave a handful of fruits on,this year and remove all others.