The Humane Society reports that the grieving process typically begins with denial, then moves into anger or guilt. From here, your friend might start to feel depressed once she comes to terms with the death. As she goes through the mourning period, you can be there for her by providing emotional support.
Encourage your friend to talk through her feelings and let her know that you're willing to listen. HelpGuide.org states that the grieving process is different for everyone - the period varies and it may take some time before your loved one is willing to talk about the loss of her dog.
Once she has come to accept the death, you might want to advise her to speak to a psychic who specializes in animal readings. A phone psychic reading can potentially put her in touch with her dog on the other side and give her peace of mind.