Sounds like Emergence by David Palmer. Also subject of this question, which means it would be a duplicate if you accept this one as valid.
The wiki entry contains most of what you remember, from the biological war:
The following day a worldwide attack, featuring a bionuclear plague, wipes out virtually all of humanity
Preteen girl being a 'mutant':
Candidia Maria Smith-Foster, an eleven-year-old girl, is unaware that she is a Homo post hominem, mankind's next evolutionary step. Hominems have higher IQs, they're stronger, faster, more resistant to illness and trauma, and have quicker reflexes. Their eyesight, hearing, and sense of smell are superior as well.
Has a parrot:
With pet bird Terry, a Hyacinthine macaw, her "lifelong retarded, adopted twin brother," who tends to "parrot" Candy's words even before she speaks, she survives the attack in the shelter beneath their house. Emerging three months later, she learns of her genetic heritage and sets off to search for others of her kind.
Written entirely in super terse style:
The book is a first-person narrative, written in the form of Candy's journal, in what used to be referred to as "telegraphic style", which is based on the means employed by those sending telegrams via Western Union late in the 19th and first half of the 20th centuries to save money. At that time telegrams were the quickest way to transmit hardcopy messages over significant distances. They were expensive; Western Union charged by the word. Hence unnecessary words were omitted: pronouns, conjunctions, most adjectives and/or adverbs.
The primary narrator's voice in Emergence is thus a sort of "verbal shorthand", and she wrote her journal in Pitman shorthand.