I'm trying to figure out what set of tools would do best for creating dolls. I figure Weaver's Tools is best for Plushies and Rag Dolls (and similar soft toys), but what about porcelain ball jointed dolls? Tinker or Potter? Maybe something more customized?

I would agree with Weaver's Tools for your soft dolls, Tinker Potter or Glassblower's Tools would probably work best for porcelain style dolls as you thought, and if you were thinking of making wooden toys or marionettes I would recommend Woodcarver's Tools.

When in doubt, Dungeon Master's discretion should take precedence, although any of those can make sensible arguments.  I might also recommend proficiency in Performance if you plan on putting on plays or shows with the dolls you craft, or Persuasion if it is more a traveling doll maker/shopkeeper style.

Thanks for the input!

Also note that some DMs may opt to give you a more directly relevant toolkit - something like a "Dollmaker's Toolkit", which includes tools relevant to your chosen profession (and grants you your proficiency modifier for any rolls relevant to making/repairing dolls :p ).

I'm no expert in doll making but have sewn a stuffed toy from fabric, however as pointed out there are many many ways of making dolls - wood carving, porcelain/pottery as well as textiles. I'd look at a similar but related proficiency and 'side load' dollmaking as the specialisation. After all if you can sculpt a dolls face from clay using [pottery] you could probably make a pot or plate!

So, I know this thread is very old but I have a question to ask. What ability score would you use (other than DM discretion) for using doll making/weaver's tool? Would it be dex or intelligence?

Quote from Ignius_Kagami >>

So, I know this thread is very old but I have a question to ask. What ability score would you use (other than DM discretion) for using doll making/weaver's tool? Would it be dex or intelligence?

I would almost always call for Intelligence. Crafting of any kind is far more a mental task than a physical one. You are of course using your hands to do things, but only baseline manual competence is required, and being really agile isn't going to increase the quality of the work nearly as well as a keen mind will.

Unlike skills, (most) tools don't have a recommended ability score (thieves tools are the only real exception, which many but not all published traps and locks specifically call out as a Dexterity check). I could see Dexterity, Wisdom, Intelligence, or even Charisma all being useful skills when crafting something small or artistic, strength or constitution when forging, etc etc. When in doubt, just let the player pick an ability score of their choice assuming they have a halfway plausible justification for how its useful for that craft. 

Quote from Ignius_Kagami >>

So, I know this thread is very old but I have a question to ask. What ability score would you use (other than DM discretion) for using doll making/weaver's tool? Would it be dex or intelligence?

 Xanathar's has almost (but not quite) no guidance for this, but here's what it does have:

1. When using proficiency in Calligraphy to decipher a Map, it's Intelligence.
   1. When you do the same thing with proficiency in Maps (i.e. Cartographer's Tools), no guidance.
2. When using proficiency in Cobbler's Tools to make boots with a hidden compartment, how well the compartment is hidden is Intelligence.
   1. When you do the same thing with proficiency in Leatherworking (or Woodworking, if you're building it into a wooden sole), no guidance.
3. When using a Forgery Kit in general, how hard to spot as a forgery the forgery is is Intelligence.

Finally, the PHB has mutually contradictory claims that both Charisma and Intelligence are the appropriate ability for a Disguise.

I think the overall implication is that most tools are intended to default to Intelligence unless you have a good reason to use something else.