the answer can't be, "just let her be with you 100% of the time."
Not 100% of the time, but when you are home, let the dog get used to being "on it's own". At your dog's current age, toileting is not going to be "spot on". Clearly you will need to address taking the dog out in an attempt to avoid accidents. Other than that your dog should be given an opportunity to "explore" her home without being in a crate or pen. Using baby gates might be a good option to keep the dog in one room. Ideally, you want the dog to be in the same room you are in, even if your attention is not fully on her. This shouldn't be a problem if the room has been "puppy-proofed". She will learn what is "ok" and "not ok" over time. But she won't learn if she is confined to "x" amount of square feet in a pen.
Any suggestions for how to help her with separation issues?
Place her in her crate, tell her you will be "right back", and leave. At first, go to the corner and back, then gradually increase the time you are gone. But you have to actually be gone. Dogs can hear incredibly well. So, if your dog is in the crate and you are fixing a cup of tea, the dog won't understand why it's in the crate.
This is something that has to be modeled on your own life. What expectations do you have about your dogs behavior? Watch your dog for cues, they have a way of training you, too.