You don't mention any other people or cats living in your house. Assuming that's accurate, you are her only family. She's just a baby who wants to be near someone else, and the only other living being in her home is shutting her out. I bet you'd cry in her position too.
Instead of locking her out of the room at night, try locking her in with you. You may think this is counterproductive, but at her age, training her to sleep through the night will go much more quickly than it does with an adult cat. Let her in and keep her there; minimize the stimulation available (few toys, no noisy ones) and maximize the ability to remain in the room (water, litter box). Give her some comfortable places to sleep, and allow her the bed as an option.
Before bedtime, spend some time playing with her. Use something she can chase and pounce like a wand toy; you want her to burn energy. After a good play session, head into the bedroom, give her some food, and go to bed. Give her some calming attention (pet or cuddle her, but don't play even if she tries to initiate). Once you turn off the lights, ignore her. Even if you're still awake, pretend to be asleep and ignore her. Again, in the morning, don't let her get you out of bed; make sure your alarm is the reason you're getting up, not because of anything she's doing. It will take very little time before she learns that she can't get attention from you, and starts to either sleep, or quietly occupy herself.
Counter to most people's perceptions, cats are not actually nocturnal; they're crepuscular, active at dawn and dusk when their prey is most likely to be active. They spend a great deal of their day sleeping, and it's fairly trivial to condition them to overlap those sleep hours with those of the humans in their household. The key is consistently ignoring their efforts to wake you. That means no yelling at them, no spray bottles, no noisemakers.
The only exception should be if they are doing something truly destructive, in which case you will want to get up, stop the behavior, briefly scold them (a sharp "no!" is generally sufficient), and then get back into bed and pretend to go back to sleep. If you get up, focus a lot of time on stopping them, and then stay up, they will continue that destructive behavior--it got you out of bed and paying attention to them, after all. If you don't give them what they want, they'll abandon that tactic fairly quickly.
Within a couple of weeks of consistent behavior, you should see her start to sleep through the night with you; if you keep it consistent, it's very likely you'll be the one who is awake first and be waking her up in the morning, rather than the other way around (this is currently the case with all of my cats). As long as her basic needs for water, toilet, and companionship are being met, she should be perfectly content to quietly sleep.