Hey Shirley,
Thanks for your question! Working with Home Children is hard but very rewarding when everything clicks into place. Fortunately there is good documentation for the children brought over from the Orphanages, like Bernardo's. There could also be some Ships lists from which to work.
Here is the British Home Children Site to look through.
Also Library Archives Canada has information to help in your search.
I am not sure about very young children being transported - the ones I have researched were not infants.
A tantalizing birth registry is just that, tantalizing until it can be proven. If you don't have strong evidence for this being the birth of your Annie, you might want to remove the Location and add a Research Notes section to the profile biography to show the pros and cons of the information you found and your theory as to why you think it might be right or wrong. This way other researchers can follow your research theories and help out if they come across something to add.
For so many of the children the path they took once they arrived at their destination is the hardest part to know. My Home Child's brother took off once his ship landed and has completely disappeared. The situations they grew up in once they were here? Most were treated as less than servants.
I know Robin mentioned DNA in her answer, DNA might be the only way to track down this lineage. If you need help with that we can get you rolling in that direction.
Try looking through the information in the links I posted and shout if you need further help,
Mags