Work Experience Cover Letter (HELP)

Hi, I am writing a work experience cover letter to The Royal Melbourne Hospital. I hope that you could provide me with some advices on how to perhaps improve this letter. Thank You

( my address)

(date) <--Is this the date I am going to post this application?

(receiver)<-- what happens if I don’t know their name?

Dear sir/madam,

I am writing to apply a work experience place at The Royal Melbourne Hospital in the department of allied health between 24th of June 2013 to the 28th of June 2013. I am currently a year nine student at **** high school and going to be in year ten next year (2013). From a very young age, I have always been motivated to assist the needy, I feel pleasure after I have helped people and because of this deep passion of helping people and finding happiness in people’s happiness, I want to pursue a career in the medical field and I believe that this work experience will give me an insight of what it is like to work in a place where many people in need are always getting help from passionate, caring and attentive personnel.
I understand that you may not be able to accommodate five days for me due to the limited positions so I would even appreciate a day or so working at Royal Melbourne Hospital.

I very much look forward to hearing from you.

Yours faithfully