How do I let someone down gently that already has low self esteem?

Yeah, there's no letting someone down gently who is in love and you're her best friend after a week. Unless she deals with whatever is driving her, it doesn't get better - at this point it should be moonlight and roses, and she's talking about suicide??

You can't fix this, believe me. Back away and don't look back. Do it nicely but firmly - tell her specifically you aren't interested in pursuing this relationship any further and you won't be seeing her again. Period. Don't listen to the tears or excuses or threats. Stop calling/texting/email, stop returning hers. Any sign of "nice" once you've told her it's over will be taken as "oh he's changed his mind" and it will start all over again.

Don't explain or try to justify your decision - she will do everything possible to shoot holes in it and make all kinds of promises if she gets a hint that you might change your mind. Also, don't go to her house to end it, and don't end it at yours. Find neutral territory and you meet her there, don't ride with her.

And yes, absolutely, if she threatens to kill herself tell her you are calling 911 - then do it. Tell them where she is and what she said to you. Remember that whatever choices she makes are due to her own illness, not you.

This isn't about low self esteem. This is full blown mental illness, specifically borderline personality disorder.

She sees you as the greatest person ever right now and in a few weeks/months she'll turn on you and devalue you and make you out to be the devil on earth.

She is a trauma survivor and you need to nip this in the bud NOW before she gets any more inflated ideals about you.

If you know her family, tell them what is being said and how you're breaking off the relationship then ZERO CONTACT.

If she calls, don't answer. If she shows up at your house don't even say anything, close the door in her face.

ANY contact, each word, will string this along for another week.

So saying, "I'm sorry." before closing the door will add 2 weeks to getting her to stop after you tell her impolite terms to please stop contacting you.

When you tell her family/friends she'll deny everything because she doesn't see what she says/does as abnormal and sees the world as attacking her not her evoking these things from the world.

Her brain is broken.

No hyperbole.

Treat her as such. If she says "I'm going to kill myself." then tell her you will call 911 immediately. If she does self harm, it isn't your fault.

And remember, her family broke her, so they'll most likely turn on you for bringing this to their attention.

If you have access to other people in her life like best friends, or family let them know how she talks to you. Let them know you're planning on letting her down but you're concerned about her behavoir.
In the meantime I would just let her know that you her manic actions have scared you off and you wish her the best. But seriously TELL someone in her family or a best friend - because I BET once you call the police or tell her family she will be like Oh no that's not me.

Don't know what your expecting here is pretty obvious the only way to deal with this is to tell her.

"Squeekie" has VERY GOOD insight and you really should listen to what s/he said. This girl did not break in the seven days since you met her, she broke long ago.