So, first off, would you like some tips on how to write a cover note? Then Frizzelle is your man. Culling advice he has provided in a book co-authored by him, he suggests that if you really want a job in writing...
...you should just start writing — and publishing. Get a blog and make it good. Make it so good that an editor who reads it will be so jealous you're not writing for them that they'll hire you. Once you already have your own writing underway, sure, apply for an internship at the place you want to work. But make sure your cover letter doesn't make whomever ends up reading it want to die of embarrassment.
And then come a few tips (but not all — for that you will have to buy the book).
One important tip: "Cool it on the superlatives." To find out why, read Frizzelle's post here.