Please do not beat yourself up hun. If he was 12 weeks old and that small this could signify a problem with his growth.
Sounds like you did everything ok, did you spray his viv so he could lick water off surfaces?
I had a beardie that did the same as yours and also died, then another I got from the same clutch died too! Turns out most of clutch died. Obviously a clutch problem. So letting the shop know in any case is a must. A PM would let you know, the odds are he was a weak one. I so feel for you and wish you luck with another beardie hun. I have 5 horrors which eat me out of house and home LOL.
RIP baby Stanley.xxxxxx