Instead of resigning, you should apply for unpaid leave of absence in the hope that your employers will keep your job open for you. I've edited your letter to this effect, including a phrase indicating that you may be able to return before three months have passed.
Due to the recent disaster following the earthquake, I need to leave Christchurch for up to three months, though I really want to keep this job which I am passionate about.
The reason why I am writing this request for unpaid leave of absence is that my parents have asked me to go back home for a short time. I am the only child in my family, so I don't want them to worry about me.
Please accept this letter as formal notification that I am leaving my position with xxx company on 7th March.
Thank you for the opportunities you have provided me with during my time with the company. I would like nothing more than to return within three months if you are kind enough to keep my position open.
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