Ok I'll have a go.... Presents on my birthday was one of the highlights of the year. I loved it as a little child, I remember looking forward to it and remembering it afterwards, and the presents were a big part of it. The sheer joy of seeing the pile of things wrapped up just for me, with brightly coloured paper and a surprise inside was so special. I feel that to decide because you felt sick, that dd shouldn't get the same joy is sad.
As a parent I sometimes have inwardly groaned at certain presents - I have three boys aged 17 and twins who're nine (whose birthday is just after Christmas) so we've had our fair share of plastic crap and guns, and my flat is small, but if they are a shit toy, then they won't get played with, and I've given them away to better places after the boys tired of them - saying that, some horrible little toys have been huge favourites, and given hours of fun, so who am I to say. At times I've steered people who wanted to buy stuff, in a certain direction eg Lego mini figures or suchlike, or even sweeties in some cases. And a party is one way of creating nice memories, but without the presents, you are setting it up as different, and yes, as others have said, worthy - in a smug way. If you really wanted to not have gifts, there are a billion other ways to have a special day without drawing massive attention to the fact she can't have gifts.
To try and sum up my garbled thoughts - it feels as though you are robbing your dc of a traditional and joyful rite of passage. There's a reason it's been done for years, and is tradition, and that's because it's bloody lovely to get presses on your birthday and at your birthday party.
Chiefly, that the sacrifice you're making, is on dds behalf, not yours, and you will actually benefit from this in your eyes, by not having to feel the feelings, deal with unwanted stuff, and get the pleasure from being worthy.
Phew, I hope that makes sense.