If it's totally clear one is talking about Christmas, your choice is fair enough.
Otherwise, I suggest donum Nativitatis.
First of all, the only alternative to donum would be munus, but this has many other meanings, and most importantly even in this context it often has the specific connotation of a favour.
As for Natalis or natalicium, I prefer the genitive of Nativitas because the former usually mean a general "anniversary" if not "birthday", and in fact donum natalicium would normally be understood as "birthday gift". The Carmina Natalicia by Paulinus of Nola (355–431) were "anniversary poems" in honour of St Felix.
While Nativitas is also not totally unambiguous, when capitalized it is more easily recognized as Christmas even without specifying Domini or Christi.
I've found three amusing websites that talk about dona Nativitatis - see here, here, here.