You need to do what is called a "second parent adoption"...this will allow your partner to have full parental rights of a child that is not biologically hers. You'll absolutely need a lawyer to navigate this process. I have represented clients in second parent adoptions, and I know other practitioners who frequently do second parent adoptions as well.
In addition, you may want to ensure you have things such as wills in place as well.
DISCLAIMER: Brandy A. Peeples is licensed to practice law in the State of Maryland. This answer is being provided for informational purposes only and the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship. For legal advice relating to your specific situation, I strongly urge you to consult with an attorney in your area. NO COMMUNICATIONS WITH ME ARE TO BE CONSTRUED AS ARISING FROM AN ATTORNEY-CLIENT RELATIONSHIP AND NO ATTORNEY-CLIENT RELATIONSHIP WILL BE ESTABLISHED WITH ME UNLESS I HAVE EXPRESSLY AGREED TO UNDERTAKE YOUR REPRESENTATION, WHICH INCLUDES THE EXECUTION OF A WRITTEN AGREEMENT OF RETAINER.
You absolutely should have a lawyer that specializes in this area. And there are only a few. We do not do this work, but I am glad to provide you with a referral?
I would like to reiterate what my colleagues have said. You do need to do a 2nd Parent Adoption. Please don't put this off. This is more important for your family than any other financial need you may have. This is the only way the non-birth parent will have legal standing to assert her rights as a parent before various institutions such as Child Welfare, the School System, doctors and hospitals. Furthermore to secure your child's right to inherit from that parent you need the adoption. The term "legal stranger" is an important one and doesn't really convey the wide gulf that will exist as a matter of law between that parent and the child.