School year still starts in August - usually mid-August. Basically, the system makes it so children start school at 4.5 years old or older. So, my daughter was born in March, so she'll be 5+5months when she starts primary school.
It's just that your son draws the short straw

From what I can tell, he won't be tested - kids in primary school are mostly put in age appropriate years and managed from there. They may test him once he's there to see if he's a 'dolphin reader' or a in the 'rainbow maths' group, etc - if you know what I mean.
Popular suburbs of Glasgow includes Bearsden and Milngavie - I'd defo look there first. Well to do folks, would be an easier-ish transition for moving from the states to Scotland.