I agree with NiteNichole. Your DD is only three. Six weeks away may as well be a year. Plus, I would be happy she isn't in "gimme" mode at all.
Our family doesn't make a huge deal about the gift aspect of Christmas. We decorate the house about a week or two before Christmas, we have a few family Christmas parties, including hosting Christmas for our family every year. When I was a kid my parents went WAY overboard on the whole Santa Christmas thing. They did everything in their power to make sure no one told me "about Santa" and even used Santa as a way to control behavior. As a child, I felt I had to go overboard on being gushy about every single present, even though I didn't feel it. And, when it was made clear, both from other kids and my own discovery (why does Santa bring Fisher Price toys if the elves make the toys?) I was crushed and actually went into a depression.
So, as a result, my DH and I have never made a big deal about Santa or the "getting stuff" side of Christmas. We do take names off of the Giving Tree at school and our local supermarket, my kids really get into buying groceries for those less fortunate than we are, they love to help with baking and even cleaning up after Christmas dinner. But,we downplay the whole "getting gifts" thing a lot. Of course, they get stuff at Christmas, but we make it more about the meaning of Christmas, both religious and secular. I don't know what your faith is, but every year for as long as I can remember, I make two "Baby Jesus Birthday Cakes" for our two big Christmas parties. I decorate them with fondant and at both parties all the adults and children who want to sing while we light the candles for Baby Jesus. For us, that's one of the heights of our Christmas. If your faith is different, you may want to discover an other aspect of Christmas that appeals to your family that you can highlight.
But, again, she's only 3. And to a 3 year old Christmas is still very far away. She will probably get more excited as Christmas gets closer. I know I certainly am not in a Christmas mood yet. We are hosting our families HUGE family reunion Christmas party, and my DH mentioned something about by securing the venue last night (our house is not conducive to a party of 70 and more people, so we have to rent a place. Already picked out, but they only schedule 4 weeks in advance) and I almost bit his head off because it's too soon!