They are not allowed in stores like that but if you get a carrier that looks like a purse (and your dog is quiet) you can probably sneek them in. Don't take your dog out in public until it has had all of its shots though. It could easily catch something.
i think the reason those pictures were blurry is because i didn't have the flash on so it didn't hurt his eyes but i do have a few where I don't think are blurry because the flash is on... but you'll have to see for u'reself... here yah go:
I love what your furbaby has done to the potty pad in that pic!
In answer to your question, I wouldn't take your baby anywhere until he/she has had all shots... it's too easy for them to catch something otherwise - and they're so little that they have very little to fight it if they do get something.
I live is Australia, and here there are very few places that you are allowed to take your dog... so I can't help you with where you can take your baby