No idea whether or not you should buy when dc goes up half a size - I tend to ask ds1 how his shoes feel and if they feel tight then I will (especially if the season is about to change so he is about to need heavier /lighter shoes IYSWIM) but if he is happy then I will get another week/month of wear out of them.
I am also suspicious because invariably he gets measured as being different sizes in different shops - 3 different sizes on the same day when trying to track down a clarks shoe that fitted (and on that occasion he really had grown out of his shoe and did need new ones. I ended up taking them back a week later as he complained the new ones were tight and he had been sold some that were much too small apparently - whereas the doodles things he got at the same time were too wide and not holding on very securely But at least they changed the shoes (unfortunately he had worn the doodles out to nursery the day before and instead of putting wellies on to go out after the rain they hadn't so they were covered in mud...)
Sorry, got diverted.
What I meant to say was remember there is supposed to be a difference between clarks and startrite sizes. I can't remember if it is a size or half size, and if it is different again for slippers, but it does mean that if you know you are a 6 for example in Clarkes then you would start looking at a 5 (or 5 1/2, sorry I can't remember!) in Startrite.
And the other thing is that different styles come up differently, to accomodate the wide variety of foot shapes as well as sizes. So sizes are only really a starting point, a size 6 in one size might be right for one shoe but in a different shoe or sandal you would need a 5 or a 7.
Not much help I know when trying to buy shoes or especially order them online!