Hehe, we share different opinions on this, i tend to believe a puppy should socialize enough before 16 weeks. Of course, you need to be extra cautious when you do so. Why? I think i am the one more likely to bring virus home through various medium, there is no 100% to say if you keep your puppy at home then they will be safe, some risks have to be weighted and taken for a brighter future of your puppy  

hey...welcome to the club. What makes u finally succumb to this temptation? What colour? U not scared short legs, long body will look like 'sausage dog'? LOL...later look like my miloboy, short legs.

Waa Kelvin, wanna adds on another family member huh? 

I'm sorry but  poodles with short legs... It takes away all their elegance, grace and beauty. I just don't understand what the appeal is. I know of one poodle who has an extreme form of dwarfism (through no fault of the breeder) and he is cute, but i would never want to see it becoming a trend the way poodles with short legs seems to be in this country .

As far as taking your dog out before all the puppy vaccinations are finished, i think it is up to each individual owner to decide what is best. Obviously pet professionals will always tell you not to at all, 100% stay at home unless really necessary, however this is because not all people will consider the risks properly and will want to take their 2month old puppy everywhere they go (which is definitely not a good idea).
In my grooming place i will groom a puppy as long as they are in good health, not overly tiny and seem strong and alert. I do however discuss the potential risks with the owner and ensure the owner gives me enough warning that i can fully disinfect any area the puppy might go before they arrive in the shop.
As a groomer it is a tough balance to find as starting a puppy on grooming when they are young makes it more likely they won't have issues with it, however health is number 1, if the owner can wait longer until grooming, i always encourage it.

650g is crazy small at 12weeks. I would be worried about the health of the dog as it grows up. For tiny dogs a simply cold can be life threatening. Also their bones are much more fragile (in most cases) and can be easily broken.

The decision is yours of course, i have my own tiny poodle (although her weight seems to have stabilized at 1.2kg so not so tiny) but i do worry about her and constantly watch for signs of fainting, illness or injury (especially as she insists on bouncing and wresting with the rest of the pack).

As long as you are aware of the issues that can pop up with tiny tiny dogs, i'm sure she/he will make a fabulous addition to the family (my tiny girl melts my heart and really is one of a kind).

KELVIN, tis one...