Phoenix,
It is good that the one you referred to, is not your boss. That is what I was wondering before I repying.
What I would do in your situation, is to gather my courage, rehearse beforehand, and ask to speak to my employer/supervisor in private.
I would tell her something like “I know how it must look with my being a new person just having been hired, and a large sum of money suddenly gone missing, where it hasn’t before”. "I know I am not being accused, but I just thought it was very important for me to tell you honestly, and directly, for the record, that I did not take the money”.
I would do this personally for myself, only because I feel it is better than those silent (yet loud as thunder) insinuations left hanging. Sadly, sometimes the awkward quietness can be mistaken for guilt.
That is all you can do, and you know you’ve stood up for yourself. I know everyone is different, but if I were an employer I would really appreciate this comment from the new person.
Since the apparent old trick of stealing when a newbie is hired might not happen a lot at a postal outlet (don’t know) your boss might not be aware of this. But still she might be aware of it just from other life experience. If she is observant, she should also be aware of the attitude problem of the young woman that you speak of, and be able to include this in the mix of things. It really does seem like a very immature, impulsive thing to do, that kind of would stand out to me as being in character with someone I knew to be a bit immature… But it is difficult to say how the supervisor views the 24 yrs. old.
If it is legitimate that money is really missing as opposed to a transaction or counting error, the supervisor no doubt, will be keeping a closer eye on things. If so, nobody will try it again, or they will, and they have a higher chance of getting caught. If it went on, with today’s technology, they could eventually figure it out.
One can buy camera’s that fit into anything. In fact, if it happened again, I’d go to my employer and suggest the idea that they put in a hidden camera to find out who is doing it!
About leaving… This is a tough one… Like you say, who needs the agro… On the other hand, it might serve you to stay a little and see what happens. Just like you elude to, sometimes standing our ground can be looked at as something
we are doing for ourselves, to grow and to feel good, instead of
"something we are putting up with." That shift in view makes all the difference, and I’m trying soooo hard to remember this too, as I start my similar venture in just 48 hrs.- gulp…
For me, staying would depend on my mind-set… If I was already in a very, very overwhelmed mode in general, with a lot on my plate in life, I’d probably plan to leave, and see what the next job would bring me. But if I was in an okay mindset in general in life, I’d stay and try to learn about myself, and how I can handle these kinds of things, and grow.
There was time where I’d always just leave uneasy situations, but now I feel it honestly would serve me the best, if I could stay as long as I can, and practice handling these things. I’d always have the ace card (knowing I can always leave down the line) tucked within good reach.
I sooooo much don’t want to listen to my own self & what I wrote above (because it’s scary) but I honestly do think it is the best road to building confidence.
Anyway, that is what I would do, personally. Talk with my boss, and then handle the co-worker situation Sandy H. style

You already showed indifference by not mentioning anything to the co-workers…
I’d stay for sure until the trouble maker leaves, as I mentioned, things might smooth over without her presence, you just might get along well with the other person.
At the same time, it doesn't hurt to keep up with the job boards & classifieds, just so you know what is out there and what some of your other choices might be, should you want to use them.
My thoughts are definitely with you... We can send each other vibes of strength and courage
If you feel like it, I’d be interested in knowing how works out…
BT