I don't think it's rude to refrain from sending her your usual holiday card this year. I'd presume she's already feel "out" of the usual holiday spirit, and that therefore it actually might be a little insensitive to send a typical, cheery "Merry Christmas!" card when she knows that you know that she just lost her brother.
You'll be sending her a condolence note, won't you? -- so she'll know that you're thinking of her. Maybe you could add something about keeping her in your thoughts "especially at this time of year" or something like that, to acknowledge that it is the holiday season.
I'm so sorry for your friend's loss.