That's about the right amount to use of each. When making ginger beer I usually use fresh, peeled ginger that I'll slice thin and put in the last 10 minutes of the boil. For yours I'd say about 1/2-1oz of fresh so it doesn't become overpowering.
You may also want to add some whole nutmeg for additional holiday spicing. One that is slightly crushed will add just enough flavor. Or, if you want to use ground, maybe 1/4-1/2tsp depending on how strong you want it. Ground allspice in the same quantity is also a nice addition.