Hi R..
First, the reason I am responding to this is because I am a nurse with 19 years of experience in Pediatric nursing and another 21 years experience in hospice/palliative care. In case you have not heard of hospice, we provide care to the dying and their families. In addition, my first husband and father of my son, died 3 years after we divorced and I had to deal with my then 12 year old son's responses to his death. I guess I just want you to know why I think I can comment on this.
When someone closely related to a child dies, the child has the right (and ultimately the need) to know what happened and if the death is an expected one the respect of being made aware of the approaching death and of having questions answered. In your case, the person who died had a significant relationship to her in a biological sense, but not as much so in the emotional arena. Your partner has taken on the role of "father in residence" and from what I can gather is filling that role adequately. All that means she may have some surprise and sadness at learning of his death, but at least in the short term you may not see any significant changes in her behavior other than perhaps a bit more clinginess to you and your partner. She may need reassurance that while people DO die; it is much more often due to disease and/or old age and that you and her Daddy are young and healthy and (hopefully) doing your best not to be involved in unsafe situations in a car or otherwise.
As far as telling her about the death, there is no rush but don't wait too long. Take your cues from her. Pick a time that seems right...a time when you would logically be talking about him, for instance; or do it when she asks about him next. When you talk to her do it matter-of-factly (I don't mean coldly) and speak to her with words she can understand. She is 7 years old and at that age children have very little real understanding about what death is or that it is permanent. If you feel emotion or the tears come (and they might), that is ok. Give her the information briefly and use words that are clear to her. DON'T SUGAR COAT IT BY AVOIDING THE "D" WORD. Children have very fertile imaginations and can invent fantasies far more scary than any reality about death that we can present them with. I do not mean give her a lot of clinical details if you know them. Just don't be afraid to use the words death and died. Avoid the words that people often use like "passed away" or "went to sleep". Children also take things very literally and may respond to being told that someone who died is "asleep" by developing a reluctance to go to sleep themselves, for instance.
Then, be available to her and supportive of however she reacts, which may be very little right now. Young children are not capable of sustained grieving even when the death is of someone who has been in their lives every day. One minute they may be crying over the loss and 5 minutes later playing as if it never happened. (That, by the way, is sometimes very hard for a grieving mother to understand.) As time goes on, she may have questions. Answer them factually, but simply and only answer what she asks. Children can't handle and don't need explanations in great detail (remember the old joke about "where did I come from, Mommy?). If she wants to know more, she'll ask more.
What you should be prepared for is that as she grows up, she may revisit the loss, especially at certain times when having him around and in her life would have been important to her...a father-daughter banquet or her marriage. However, having your partner there in the role of Dad may help fill that empty space for her, assuming their relationship is a good solid one. Plus, I really do like Angela's suggestion about collecting any information or momentos you may have to give to your daughter when she is older.
You should also be prepared for the very real possibility that you may find yourself grieving, even though the two of you had gone your separate ways some years before. There was enough of a connection to create a child together. It is ok for you to grieve, but be aware that you may not get much sympathy or support from those around you, including your partner. The world at large sees you as having severed the relationship and so assumes that you have no reason to care what happens or happened to your former spouse/partner.
I hope this helps and my condolences to both you and your daughter. B.