I have a new puppy that I borught home 4 days ago. She hasn't really been eating much. I bought the same food she was being fed at her old home and have even tried other approach. I just worry that she will beccome ill. Will if be fine to supplement her dog food dry/wet with milk replacement?

You really don't need to. A 13 week old is well past needing milk. Four days seems a little long for the new home effect. I would get her to a vet as soon as you can without seeking emergency services. For more details, see the sticky, https://www.askmehelpdesk.com/dogs/information-articles-our-dogs-expert-labman-53153.html#post254171

If you check the ''What does a puppy need?'' section too, you will see I recommend sticking with what the breeder is feeding. The worst thing you can do is get started on rich food. A healthy dog will eat dry dog chow, and a sick one needs a vet.