Sleep

At what age can we truly let our breastfed babies sleep through the night? I have a three week old and I was told at her 2 week appt not to let her go more than 4 hours without eating. So I set my alarm at night just in case and last night she was sleeping so well that I had to wake her up to eat at 2am. I really wanted to just let her sleep but I was afraid to. At what age is it safe to let her sleep?