When you put her out during the night - go with her and as soon as she's done, bring her straight in again, and into her crate, with a biscuit if you like. NO PLAYING. Shut off the light and go back to bed until it's time for you to get up. I had my puppy's crate by my bed, and set my alarm for around 4/4.30 to get her out. And I tried to anticipate her waking so she didn't get the mind-set that whining and carrying on was going to get me up. At 8 weeks they can't hold all night, but once should be enough to get them out otherwise they won't learn to hold.
Unfortunately some puppies make more noise than others, especially when crated. How long are you crating her for during the day? Puppies should not be crated for longer than 1 hour at a time, at this age. Otherwise it's crate abuse I'm afraid, and small wonder she'd be whining and barking. Cover the top and three sides of the crate and have it in the living area during the day with the door open, so she gets to use it as her bed. When you have to go out, shut the door, but don't leave her, for now, for longer than 1 hour. You can gradually increase the time you are away as she gets older, but adult dogs should not be crated for more than 4 hours at a time on a regular basis.
A dog is not a caged bird, and forcing them to spend long hours caged is cruel and abnormal, for a dog. If they have to be left for longer (not good, dogs are social animals and need their 'pack' around) make a room safe for them, or a pen with far more space than a crate.