Do you think I should tell my friend that I don't think she's ready to have a dog?
What makes you think your friend is not ready?
Because I think she's the kind of person who's not responsible enough to take care of a living creature.
Telling your friend what to do with her personal life is intrusive. You should avoid doing that unless your friend specifically asks for your input.
I bet she's not going to be able to handle having a dog.
That may be the case, but even if she isn't it is not your place to tell her that you don't think she should have a dog. Your friend wants your support, not your criticism.