That was the same as me when I was pregnant with DD2.
My Hb level was already under 10 when I was newly pregnant with DD2, so started on Ferrous Sulphate almost immediately.
I had 200mg to be taken morning and evening - like you had no problems with constipation although my morning sickness was a LOT worse with DD2.
Good point from Stace - make sure you take them with fruit juice - not when you have your tea/coffee!