Close, but your example is missing a crucial piece. Specifically, the marginal cost of producing the product.
Let's say the MC is 20 cents at the scale produced (Q1). The second group (students) get a MB of let's say 30 cents. They will not buy at a price of 60 cents, therefore there is a deadweight loss (MC < MB to students, but they do not have the good). If the monopolist can expand their output to Q1 + Q2 (where Q2 is the student sales) while keeping their MC under 30 cents, they can reduce the DWL.
Umm... so you agree? Price discrimination can reduce DWL?
By the way, there's no need to assume MC is a function of Q since that just complicates the example for no benefit (in the wiki article notice that MC is just a constant 10 cents). And yes, though I didn't stress it, of course the discount price must still be greater than the MC (and so in the range of 10 - 60 cents).
I didn't understand your argument at first; after you clarified I believe you are correct (with the corrections mentioned). My comment was intended to fix some flaws in your argument that rendered it incomplete, not incorrect.
I believe the constant MC assumption is dangerous though. MC is rarely fixed in microeconomics. It is almost always assumed to be an approximately linear function of quantity. Thus, increasing production will always increase MC. You'll need to hire more workers, pay more overtime, buy more expensive supplies, whatever (in the short run; in the long run firms expand production and the supply curve shifts). The assumption that MC won't change is almost always incorrect, and the MC changes affects whether the argument is valid or not.
Sorry if I'm sounding pedantic, just pointing out what my econ prof would've said to me about this argument.
EDIT: and I'm not trying to imply that you don't know any of this, just that it may benefit readers who have less economics exposure.
Let's say the MC is 20 cents at the scale produced (Q1). The second group (students) get a MB of let's say 30 cents. They will not buy at a price of 60 cents, therefore there is a deadweight loss (MC < MB to students, but they do not have the good). If the monopolist can expand their output to Q1 + Q2 (where Q2 is the student sales) while keeping their MC under 30 cents, they can reduce the DWL.