Perhaps things are different in the UK but I am a nursery nurse in a school and I dont know any of my children aged 5+ that wear pull ups to bed. I have two sons aged 9 and one just turned 3 both of which are fully potty trained and dont wear pull ups to bed. My 9 year old was fully potty trained by 3 1/2.
Your daughter will do it when she is ready and until then it is your decision whether or not to keep using the pull ups.
My youngest son who turned 3 in May has been going to bed with no pull ups for the last month, admittedly he had one or two accidents at first but now he is completely dry.
If I had a child who was over 5 and wore potty training pants to bed, I would be slightly concerned but it sounds like the paediatrician has stated that there are no worries. It is funny how things differ from country to country.
I am sure everything will work out ok, good luck