I would just reiterate what another mom said - your friends' kids are not your kid. Every child is a completely individual person. When you have your second baby, it will be very clear to you how different they really are. My daughter spit out her pacifier at 2 months and never took it back. She slept through the night at about 13 weeks, but had a hard time getting to sleep - she'd lie there and worry about things and keep calling me back to her. My son took years to sleep through the night, but when he was ready to go to sleep, he was out in literally 3 minutes.
If you think you're tired of it now, just wait! Having 2 babies in diapers will be an experience that just can't be described. The army has done tests showing how sleep deprivation affects people, yet moms are expected to go without regular sleep for YEARS, and keep everything together all day too.
It would be nice if babies were more predictable and willing to take our needs into consideration, but that just isn't how it works. Sorry, but your pediatrician is right.