You have a couple options here. You could make the recipe as written, enjoy one layer of the cake, and freeze the other for later. Or you can freeze everything and assemble later. If you plan to freeze half the cake (a single layer), make sure to halve the cream ingredients. Top each slice with a nice dollop just before serving instead of building a layer cake.
Now, for the freezing part: Let the baked layers cool completely. Wrap each layer tightly in plastic wrap, or place a sheet of parchment between the two layers and wrap them together. Add a layer of foil over the plastic and freeze for up to 2 months. A day before you’re ready to assemble or serve your cake, thaw overnight in the refrigerator, still wrapped, to preserve moisture and structure. On the day of serving, you can go ahead and make the cream—I don’t recommend doing that part in advance.