She claimed some Lhazareene people including Mirri Maz Duur as her slaves. Perhaps, she intended to treat them relatively better than average Dothraki would, but she made them slaves nonetheless.
Well... yeah, she was young and assimilating with that culture. It's fucked up definitely but it doesn't make her evil. Her time with the Dothraki was really the first time she was able to experience a world outside of Viserys' one, so I can forgive her for not immediately starting her crusade to free slaves and instead trying to make due with what she was given. No one's perfect, especially not at that age.
I don't know why Dany took them as slaves instead of freeing them or if it's addressed in AGOT. I can think of a few reasons she might have, though.
Freeing them would have stirred up even more, potentially fatal shit from within the Dothraki so keeping them enslaved was the safest bet for everyone at that moment.
She didn't actually have the authority to set them free, either because Khal Drogo did not allow it or Dothraki custom in general didn't allow it.
Freeing them would mean they were no longer under her protection which meant they were fair game to Dothraki who could undoubtedly ride horses and run the women down if they so chose (which they likely would).
Dany did not even consider freeing them, either because she's naive and didn't think it possible, or because she was too young to consider going against the cultural standards, or maybe she was just being spiteful for some reason.
Dany uncharacteristically just really wanted more slaves.
To me, based on her character development in later books, I'd imagine it was either a mixture of naivety and caution, or total caution.
Technically, it doesn't matter what Mirri Maz Duur's assumed crime was. Daenerys acted as a slave owner and brutally executed her slave.
This simply isn't an issue for me. It isn't even a gray matter. Based on the text I read, Mirri Maz Duur's execution was based on admitted betrayal and murder. Dany was acting as judge, jury and executioner, and I fully supported the decision. Did Drogo deserve to die? Yeah, most definitely. Did Dany deserve a forced abortion? No, and for that I support Mirri Maz Duur's execution.
The same way Daenerys was perfectly fine with her husband selling those babies into slavery to be savagely trained or otherwise exploited. Oddly enough she didn't have sudden urges to teach her Sun and Stars a lesson. She is a total hypocrite. Only a small group of slavers was involved in the Unsullied training, but she ordered to kill everybody in the city from 12 years old and up.
I don't know if I need to emphasize this more, but she was 13 in AGOT and assimilating with a culture that she had no choice but to assimilate to, at least at that time. Yeah, it's really, really fucked up, and I'm sure that she'd have turned into a hateable monster like Drogo if she'd stayed with the Dothraki for a long time, but she didn't stay and she grew up and she seems to be trying to right these things. I can't call her a hypocrite or a villain for that. It'd be like calling a 20 year old reformed homophobe a hypocrite for bullying gay kids in middle school. They fucked up. We've all fucked up at that age. But we eventually move on and the opinions should with them.
As for killing people ages 12 and up: again, she's only only about 14 in ASOS. I'd imagine from her perspective children that age are of equal standing. It's fucked up, especially from our perspective as people much older than that, but that's the truth of the matter for her. In the show, it's a lot different, but then again I don't think she says anything like that in that episode.