I think the OP is getting an unnecessarily hard time. She hasn't replied to the NQT yet. I'm sure I'm not the only person who sometimes gets work-related mails and my initial reaction and the reply I'd like to send is a lot less professional and more sweary than the reply I actually do send. I do not always immediately see a rational and reasonable way forward, but I do give myself time to think it over and let the benefit of the doubt come to the fore. Sometimes, this involves talking it over with others, as the OP is doing here.
My holidays are sacred to me and in any case, I often go to places where mobile and WiFi signals are intermittent/non-existent, so people can't contact me anyway. I don't go to places like that when I have to cover on-call or out of hours work. But it is good for me and my colleagues for me to get a real beak from time to time. We did cope in the days before mobile phones and email (though my job wouldn't exist without them.)
For all we know, the OP mght be posting using hotel WiFi beside a pool on the Med or somewhere. I would feel intruded upon if I got work-related emails to personal mail then. Some colleagues do have my personal email. In the past, I've found a reply saying, "Please don't use my personal mail for work matters, please use my work mail," works fine. (I assume the OP won't have a work email address before September though.)
So I think NQT's enthusiasm and nervousness is totally understandable, but it's also totally fine to say, planning is planned for later, will be in touch then. If NQT will be on her own hols then, she'll have the chance to point it out. But unless she reads MN, she'll probably never experience the OP as selfish, and all the other things the OP's been accused of. Just like most of my colleagues don't know exactly what my initial reaction to some of their mails have been.