Pretty much.
Although there can be a number of reasons they get up early or in the night. teething, sleep regression etc....
But it doesn't take a genius to know if you go to bed early you normally wake early.
I always try and aim for 7 or 7.30 bedtime with my little one, as hopefully she'll give me a 7 or 8am wake up.
I mean, I like my time to myself on a night but hell noooo would I put her to bed at 6.30 or earlier.
For someone who doesn't work and doesn't have her child 24/7 I dont understand how she can be so tired all the time.
Sorry for the essay