DS 4 1/2 but uncomfortable in current school

My son has become bored in current school and is acting out in a way
which makes me feel I don't want him to go back there next year as I
have decided to send him to a private school for K-8 the following
year.  He was tested and while very bright this K-8 school feels he
could use another year before going to their school.

Being it is so late in the year to get into another school around
here  and even finding one which is not cost-prohibitive and he is
technically the right age for public K, I was thinking maybe to send
him to public K (which is half day in our town)...and then move him
over to the private K the following year.  The time in school, pre-K
or K would be about the same yet he would get more structure.

Does anyone think this is a good idea, bad idea and why?  I'd
appreciate the input.