My dog followed me around constantly and still does actually, unless hes really tired. But through gradual increase and training as he grew up, I can leave him for 8 hours without any separation anxiety. Leaving the house is different, and the puppy will accept this.
However, at the moment she is just a baby, a bit overwhelmed and never been left alone before.
Give her a bit of time to settle in, then start the training.
Place her one side of the baby gate, with her bed and a chew etc.
Sit the other side of the gate, right up against the gate. Watch tv/read a book etc. Minimal interaction with her.
Then you want to sit in sight of the gate but not directly touching it
Then sit a bit further away
Then start doing some housework etc in that room, so you are moving around in and out of sight continuously.
Then leave the room briefly, back in the room.
Each time, minimal interaction with her.
To start with she will probably watch you like a hawk and be up and down every time you move. The aim for each stage is to get her settle down, not whining or fussing.
How long you need to work on each stage depends on the individual dog but don't rush to the next stage. And don't spend hours and hours each time. Once she has settled down for about 10-20minutes, you can say good girl and go in an say hello.