I will at least apply to see whether the kid is ready or not

In the States, the parents must submit the request first and then the school will gather teachers' feedback, provide testing (IQ and acedamy) as well as assign a psycologist to observe behaviors and maturity.   And they do consider the kid's height and weight to see whether they will fit in.  If school's evaluation is yes, you can make a final decision about whether to move forward or not.  In my area, the school gives one month's trial, and they assign a group of teachers to evaluate and recommend after trial period.

Unfortunately, there are always pros and cons on either approach.  If kids are less academically challenged, they could be a distractor and headache in the class.  On the other side, if kids are not mature, they could disturb the class as well.  There is not a sure answer in these cases.