I would maybe consider taking her to a vet just get her checked out and ensure she's not having any problems; IE, dry heaving. She might be having a reaction to the food you are feeding so if the vet gives her a clean bill of health I would consider switching to a higher quality food (and I do not recommend feeding the foods that vets recommend/sell). Check out www.dogfoodadvisor.com
and compare some 4 - 5 star brands in your price range available in your area.Although, I HIGHLY recommend feeding a raw diet if this is convenient for you.
Puppies go through all sorts of phases, mine would vomit once in a while after eating... but it was usually from eating too fast - I solved this problem by getting a slow eater bowl.
If she's dragging food all over the house then you might want to think about feeding her in her crate (and if you dont have a crate then I would highly recommend getting one and crate training her ASAP). This would inhibit her from playing and dragging food around. If she does not eat in the crate, take it away momentarily and try feeding later. Dont worry about starving her, if she's hungry enough she will eat..but first of all I think you should try and nail down her upset stomach and dry heaving.. this very would could be a food allergy/sensitivity.
I'm sure others will chime in with some helpful tips as well, but that's just my two cents. Good luck