One hesitates to find flaws in a heroine as sympathetic and in such reduced circumstances as Anne. Nevertheless, I believe that Jane Austen has created Anne's character with strengths AND weaknesses, and I'd like to reflect on those before reaching Chapter 12.
Indeed, Anne is very level-headed and efficient in serious matters concerning other people (e.g. her retrenchment recommendations motivated by "justice and equity" to the lenders, or her management of the situation with little Charles on the first day of his injury). But in the matters most personal and closest to her heart, she tends to act irrationally, panic and run away.
Take her avoidance of meeting with the Crofts. In the end of Ch. 4, she reasons, quite rationally, that they are not aware of her broken engagement with Wentworth and so meeting them "need not involve any particular awkwardness", which of course is a good thing, as they would HAVE to get acquainted anyway. Yet, the very next sentence, in the beginning of Ch. 5 lets us know that she contrives an excuse in not seeing Crofts: "On the morning appointed for Admiral and Mrs. Croft's seeing Kellynch Hall, Anne found it most natural to take her almost daily walk to Lady Russell's, and keep out of the way till all was over; when she found it most natural to be sorry that she had missed the opportunity of seeing them." Anne could have been one of the first to be introduced to the Crofts, and perhaps she would discover sooner, rather than later, that they were not scary at all. But she ends up being practically the last one in her extended family to meet them, after rather depressing thoughts of strangers occupying her home. Moreover, it is only after Mary coerces her husband to pay them a visit and comes back "in a very animated, comfortable state of imaginary agitation", that Anne expresses a wish of meeting the Crofts herself (Ch. 6).
When Captain Wentworth arrives in the neighborhood to visit his sister and brother-in-law, Anne thoughts are all on how to "escape" meeting him (Ch. 7). But the "joy of the escape" (provided by little Charles' injury, no less) is no joy at all. On the second day after the accident, Anne sends Charles and Mary off to a dinner with Wentworth (and they are only too eager to go) and stays in the cottage to watch over the sick child. However, the boy is doing much better at that point, and Charles does urge her to let him fetch her later that night. Yet, Anne is in full escape mode and refuses to budge. She remains in the cottage, unhappy, restless, angry with Charles and Mary for "abandoning" their child, while "being happy" elsewhere, and angry with Wentworth for "making himself agreeable to others". Perhaps, had Anne managed to overcome her anxiety and go to the dinner as Charles suggested, many bitter feelings and silent mutual recriminations could have been avoided.
Lady Russell is, of course, Anne's friend and her intentions are good, but is Anne over-reliant on her friendship? Anne is free to discuss (and criticize) Charles' choice of a wife and the adverse effect Mary has on Charles' character with Lady Russell (Ch. 6), though "unimproved" and unrefined Charles is doing quite fine. But where her own uncertainty and turmoil related to CW, issues most affecting her own happiness or unhappiness, are concerned, Anne is on her own. She cannot confide in Lady Russell. Moreover, LR does not seem to be included among those who appreciate Anne's piano playing: "Excepting one short period of her life, she had never, since the age of fourteen, never since the loss of her dear mother, known the happiness of being listened to, or encouraged by any just appreciation or real taste." (Ch. 6). The only people who truly understood Anne seemed to be her mother and Wentworth. Her mother is gone, and she is practically not on speaking terms with Wentworth, due in part to Lady Russell's interference. Yet Anne thinks "with heightened gratitude of the extraordinary blessing of having one such truly sympathising friend as Lady Russell". With friends like LR, Anne needs new friends ASAP.