I don't think so - it would seem a little OTT to send cards too as there is no way your dd could do them herself at her age. Once she's old enough to sign her own name I think it might be a nice idea as it will help teach her about manners.
No, I wouldn't send them for gifts received in person and at 2 I wouldn't send them at all. I would ring the people up and get her to say thankyou on the phone. More meaningful than a card written by you IMO.
Thanks for the responses. I felt as though it was probably just appropriate to say thanks at the time. When DD was born and when she turned 1, we were living in Ireland and so I sent thank you cards for stuff received in the post, which made me wonder. Thanks again
when my boys were smaller they used to 'draw'on a postcard which i would then send to the sender of the gift,to little friends a personal thankyou at the time sufficed but for aunties godmothrs and grandparents to this day they still send note saying thankyou- except to my nan who rather crossly announced it was a waste of first class stamp to send a thankyou card