My father was born in Scotland and then moved over to Canada when he was around 3-4 years old. He does not have a british passport but has his birth certificate from Scotland. Am I entitled to a british passport based on him being born in Scotland? And I have a 1 year old daughter. If I obtain a british passport, would I be able to bring her with me to the UK? And what would I need to do, to bring her with me?

There were changes in UK citizenship laws in recent years. I am not 100% positive but this case may not easy one. Your dad needs to verify his citizenship first then he can pass that to you and your child. Consult immigration lawyer in UK.