I think the vet is a good idea. Eating odd things and then bringing them up with what sounds to be bile can be a sign of a blockage. They eat things which they know are going to make themselves sick to try and clear what ever is bothering them.
Is she drinking more than normal? Or is she displaying any signs of discomfort - bowing and stretching?
Has she been doing it her whole life or has she recently re-started the habit? If it's the latter perhaps the new puppy has stressed her out a bit, and she's reverted back to something that was a comfort to her in the past. How is she generally with the new pup? Has anything else changed that might have triggered it?
In the meantime I'd make sure you keep things out of reach she might chew (I have labs, so I'm used to keeping everything out of reach - you do get used to it!).
Our dog (whippet/alsation cross) is 11 yrs old. She's never had any health problems, has a yearly check-up at the vets, is wormed/flea'd regularly and usually perfectly happy. For a couple of weeks she has been eating paper- white paper, homework, receipts and my lottery ticket She is sick a few hours later and it is bright yellow fluid with the chewed up paper in it. I know dogs like to chew things and she ate lots of things as a puppy- but surely she's grown out of that by now. We have a new baby and thought maybe the paper eating was a way to get attention. Does anyone else's dog do this? I'm going to phone vets in the morning to make an appt for her.