Well, how do you feel? Do you think you will feel burnt out? Plenty of people go straight into school from undergrad and do just fine. I would be thinking about the loans to be honest. I believe you have six months after graduation before interest kicks in.
Those three things he listed can be done in what, a month? I don't know about the backpacking through Europe but that sounds expensive. What will you do with the other 11 months? I ended up having a gap year and a half before I started my master's program (not really by choice, I graduated in January so that put me in a weird spot) and I spent time doing things important to me BUT I also wanted to stay in the school mode and didn't want to lose focus so I took two classes at a Community College while working to save money. I am actually finishing up another gap year since I graduated my master's program in August and will be starting school this August and spent time hanging out but I also started working in a dental office not only because I wanted to but I wanted to have something to talk about should I be granted with interviews. I didn't want dental schools to say "so you did WHAT in this year and a half?". Take a break for sure if that's what you want, but maybe also do things that will help your app and are things you like. Volunteer, work somewhere dental related, etc in addition. Just my opinions.