I am so sorry.
Please do not do that to your daughter, waiting until she goes back to school.
Include her when you have made the decision.
Our dog was ill and elderly & my father made the decision one day to euthanize, without any input. No one knew. And did not stay with her, because he could not emotionally do it (and was a time period where it was not as common). But even at a young age I could & would have stayed. Not every human has the same emotional abilities. It all sounds horrible, but he was not a horrible man - just a man that probably thought he was protecting others. And helping her not suffer, which was completely valid and the strong part of him.
But he was not protecting us, he was hurting all of us with his choice of not telling us all in advance.
I had just come home from university for Thanksgiving and I could have had the chance to say a proper goodbye to a dog that meant everything to me. Because it occurred just after I left to go back. Like the next day or so,.so most likely not a coincidence (Editing after Imzadi's post as I realized he probably chose it that way to face no emotions in the moment, but those emotions are normal) And of course he let my Mom share the news to me

over the phone - sigh, that a dog that slept with me almost every night from six to twenty-one was gone.
OP, this was almost 36 years ago! And I think you can see how it still impacts. Include your daughter.
Do not be afraid of just and valid emotions. It is completely normal with such a loss.
I think once you make the decision to euthanize you could have the tough thoughts & feelings that you might have waited too long. So bring that possibility into your decision right now. I have had that myself, wondering and wondering if it was time. Spending so much time telling myself it was not time and then suffering afterwards that I had waited too long. It is so hard at every corner.
I have such admiration for direct veterinarians and doctors. They help the process. They help take away regrets & give more peace. I wish more of them existed in this world. They are brave.
One of my pets was an at home euthanasia. She was so lovely - the vet. Made a world of difference.
I am so sorry for you & your family, all the best to you.