If you really want a mamogram, I would suggest going to another doctor for a second opinion. It is definitely not pointless. I've pretty much been nursing since I was 35 and have had 3 full checks and went back one other time for a recheck on the left breast. So that's 4 times, 3 times while nursing.
The breasts are denser due to the milk ducts, but a good doctor will be able to look at your mamogram and decifer it. Being 36 its not as important as when you turn 40, so waiting will probably not hurt.
I plan on nursing at least another year which will make me 44 and for me I'd rather have the peace of mind