Please keep doing what you are doing. Yes your beautiful daughter will sleep through and no you wont have to CC wiht her. Babies need us to help them sleep...would you sleep well if you were left to cry for yourself to sleep..I know i wouldnt. Just follow youre instincts and NEVER doubt them
Maybe drop off off a copy of The science of parenting/what every parent should know...that should help your doctor give the right info.

Your doing a great job xx