I understand your perspective and can respect why you want to do it, but your post filled me with a lot of thoughts on behalf of your daughter.
If I were your daughter, I would be confused about what getting presents at Christmas has to do with getting gifts on her birthday two months later and I would be hurt and sad that my mother barred everyone from giving me any if they so chose. Truly not trying to ask sarcastically here, but are you planning to do this the rest of her life? Another mom was right. It sounds like punishment for her.
When my children attend a party and bring a gift, I don't first think of obligation. Neither do I expect a gift from each guest when hosting birthday parties for my children. I was raised this way. If the guests bring a gift, it's an honor and a pleasure for my child. Gifts are never an obligation for any occasion; they aren't a ticket in the door. Otherwise they wouldn't be called gifts. Even though my kids are very young, I have explained this to them and will continue to do it until they can accept them graciously and without a sense of entitlement. Also, according to most etiquette I've read (and heard from my mom), it is never appropriate to suggest how people should or shouldn't spend their money in an invitation.
I'm wondering if instead you might ask your daughter ahead of time to consider which toys she owns that are no longer important to her so that she might purge some, give them to a charity and look forward to her birthday. That way she has done something good for someone else in honor of her birthday and she still gets to enjoy the gifts she MIGHT receive.
I don't mean to lecture and apologize if it came off that way, but I think you should let others decide if they will present her with a gift. Best of luck and best wishes for a happy birthday to your little girl!