Hi, you are right, she is such a cutie!
When you said that you have no say is that because your gf is deciding or the breeder is deciding! Just curious as it might make a difference in how you go about trying to change someones mind.
I got Sophia when she was 8 weeks old, and let me tell you, that was a little too early. She really had trouble eating. My very first posts on this site and why I even looked for such a site were because of her trouble eating. They are so small that even a tiny set back can cause serious medical problems.
Six weeks is sooooo young for a Yorkie. They are still infants. I beg you to really read on this site and learn all you can about Yorkies. If it is your girlfriend who wants her early then please have her read her on all the reasons it is better to wait until they are older.
If it is the breeder who wants to send her home that early I would just tell her you want the pup to stay with mom and litter mates longer. And honestly, any breeder who would let a pup go home at 6 weeks is highly questionable. If they were at all knowledgeable with the breed they would never let them go home when they are still newborns.
A six week old puppy is not even ready for real food yet and still gets it's nutrician from the moms milk. I think their little teeth are just coming in. Their digestive systems are not developed to handle commercial dog food yet.
Please, please, please educate yourself, your girlfriend, and your breeder if necessary on this issue. You may be the only hope this sweet little pup has. Be her hero.