I don't know about kittens to be honest, but I was told by the rescue I adopted Lexy from to take my cues from her. After a few days in one room, she started trying to follow me out, so I let her and kept other doors in the house closed. It took about a week after and she started wanted to get to the rest of the house, but she is still, even 10 months later, very wary of the kitchen. She always walks into the back part of the house very very slowly (she was very timid so there is a reason behind this).
Your kitten may be different. You are wise though to get her litter trained first.
I did have a funny one once, where Lexy was in her tray having a number 2 and I moved and it scared her so much she jumped out mid "business"! So I had to walk with a tissue after her to go collect the little droplet trail she left me
...thankfully easy to clean, hugely funny, but made me careful not to disrupt her when she's going....a hooded tray works wonders for this!