I don't understand the whole gift card thing.
Why not just put money into a separate bank account?
In answer to the OP, I don't start thinking about Christmas until November at least. My kids are older now, however I found when they were little their tastes always changed between the mid year toy sales and Christmas, especially as heaps of new and different toys are on the shelves closer to Christmas. I always found it better to wait.
I file my tax return in October and use of my FTB sups / tax return to cover Christmas and back to school expenses.