Well...it seems she is definitely too young to be away from her mom. I mean if she's 1 month old, she's just a baby. I'm sorry.
But don't despair. Smaller kittens have been rescued and they have survived with proper care.
I'd suggest, first of all, to take her to a vet asap. Kittens can fade away really quickly, just within hours. So a vet checkup is a great idea now.
Second, feed her as much as she can. I suggest you stop with the crunched dry food and get her a high protein canned food. This doesn't mean you have to feed her that through her entire life, but this few weeks are crucial and she needs to be fed the best food she can, considering mom is not around to nurse her anymore. I've fed abandoned kittens with Hill's prescription a/d, is not really a great food but it is great to help growing kittens. You can even mix it with some water, and put it inside a syringe, but I bet she's ready to start eating that from a dish and you won't need the syringe.
Third she needs to be warm, so maybe a heated bed of some sort, it could just be a hot water bottle.
Good luck with everything, if anything just let us know, there are many people here who can help with good advice