@Jane1122. Jane, welcome. I'd ask them to modify their booking to add three pets, as this may help more to cover you in the event of any damages. Also ask them to confirm again final human headcount is one.
If this is truly a single person spending Christmas alone then yes the dogs are their family, assume this but always check with questions. First get on their side by asking for their names and breed telling them its so you can refer to them afterwards in your review for future hosts who may also be open to hosting pets. Will they be bringing their own dog beds or using yours as 3 is a lot to cater for so maybe ask them to BYO.
I would make sure the dog clean up rules are clearly set out (or draft some quickly now). It also doesnt hurt to have doggie poo bags supplied. Most get the hint 😉
Try to balance lack of profile info with engagement. Ask them what their interests are so you can send them links and update them on local events. We hosts have an advantage in that they are booking a real person, not AI. Many guests have thanked me to help them see how to better use Airbnb for both our sakes!