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Kaj_Sotala comments on Of all the SIA-doomsdays in the all the worlds... - Less Wrong
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The main point that I get out of those examples is that the Doomsday Argument is really a fully general argument that can be applied to pretty much anything. You can apply it to itself, or I could apply it to predict how many days of life I still have left, or for how long I will continue to remain employed (either at my current job, or in general), or to how many LW comments I am yet to write...
A claim like "my daughter just had her first day of school, and if we assume that she's equally likely to find herself in any position n of her total amount of lifetime days in school N, then it follows that there's a 95% chance that she will spend a maximum of 20 days of her life going to school" would come off as obviously absurd, but I'm not sure why the Doomsday Argument would be essentially any different.
It's possible to argue that it is appropriate to use SIA in some of those examples, but SSA for the duration of the human race.
The doomsday argument doesn't say that, even if you do use SSA with the reference class of days that your daughter is in school. You're confusing the likelihood of the evidence given the hypothesis with the posterior probability of the hypothesis given the evidence.