Technically, your baby is an adult at 8 mths - but since you *just* got her from the breeder and she was in recent contact with puppies - you really should get her to the vet. It's best anyways to get any new dog to your vet asap - just to get them checked over.
I would not recommend giving carrot at all, at this time. Since you're already giving rice and chicken (and IF she's keeping it down), then stick with that combination only - until you see the vet.
Personally, I'm not a fan of Science Diet or Royal Canin - but everyone has to find what works for them. If RC is your goal, then you'd want to add it back in once you get a health 'okay' from the vet. If it were me, and if I was going to feed kibble (I feed Natures Variety Raw Frozen or I home cook for my dudes) - I'd feed Natures Variety Instinct Kibble, Canidae, Orijen, Natural Balance, California Natural - or something like that.
Plus, if I had to feed kibble - I'd add in canned food for the superior meat quality and added moisture. Please update if you can!