Is taking hair using FUE from the body to transplant into beard a good idea?

You can harvest the hairs with the FUE method.  This will give you a less visible scar.  The resulting scar will be a few hundred 1mm diameter pale "dots" spread out. There is no surgery that does not leave a scar.  As long as you don't shave your hair, you will not likely notice them.

Body hair has a different life cycle and stay in growth phase much shorter than beard or scalp hair.  That is why we can grow our beard and scalp hair long but body hair never grow more than a few centimeter (max).  The best match for beard is scalp and removing a small number of grafts through FUE (direct extraction) from the scalp will not be visible at all.  You can consider body hair only if you have very strong (thick and long) body hair as long as you understand you need more grafts to obtain the same density when using body hair as opposed to scalp hair.

In general, we do not recommend to our patients to utilize body hair to be transplanted to improve the look of their beard or hair on their head.  Typically, body hair is very different in quality from that of the facial hair or hair on the head and will not look natural when transplanted. 

I understand your concern about a scar at the donor site.  Are you aware that you can have the hairs taken from the back of your head without a visible scar?  I recommend you see a hair transplant surgeon who offer NeoGraft.  Micropunch grafts are used leaving no visible scar.  I have treated many young men who have your concerns with this method.  

If you use body hair, the character of your hair may not look like your beard hair as body hair is often finer. Also, few doctors do this very well.

Ther are a one risks involved with body transplant one of which is it may fall off in the future and it is not a permanent option. You need to do a consult with a specialist in hair transplant procedures to get the pros and cons before making a decision.

See someone who has experience in harvesting body hair for hair transplantation. To get a good result in a beard transplant, the donor hair should have similar characteristics to your beard. Your body hair may or may not be a good source for donor material.