I've had an 8 week old pup who had been weaned at 5 weeks (we rescued her). She had rickets from having been weaned too soon and it took months to resolve. She also took a long time to settle and cried a lot.
But @FrangipaniBlue, it's clearly not the case that all eight week old puppies end up with rickets and take a long time to settle in. You say yourself your puppy was a rescue - do you not think that had something to do with her health and behaviour?
I've also had a pup from a breeder at 12 weeks. I cannot even begin to explain the difference. A decent and ethical breeder would not allow a pup to go before 10 weeks old.
That's just a matter of opinion - it's perfectly legal for puppies to go to their new homes at 8 weeks so it's not fair to criticise OP for doing it, IMO. We got our puppy at 12 weeks so I'm not an advocate for all puppies being re-homed as early as possible, but I wouldn't pick at someone who did re-home that early either.
and a 9 week old pup who has not yet been vaccinated certainly shouldn't be paraded around a shop in a sling like a designer accessory FFS.
But that's not what OP is planning on doing!
Socialisation is vital for young puppies, and being carried securely in a sling for comfort and reassurance is a great way of allowing that to happen.