I show dressage in Canada and took my grade pony to gold level shows, so he has a passport. My friend also has a grade mare and she has a passport too, so your mare doesn't need to be registered to be granted one.
Directly off of the EC website:
In the case of a horse for which there is no record of registration, the application must be accompanied by proof of ownership and a sworn affidavit that the animal is not registered.
I think we got our sworn affidavit notarized with our lawyer, but google tells me you can get it done at courthouses and banks too(?). For sire and dam I would just put in unknown if you don't know, as well as N/A for registration number etc.
Here's the EC website page that includes what you need to include for a passport:Buy/Renew
Also, on the show entries for dam and sire just put in unknown. That's what I always did with my pony and I never had an issue! I
Hope that helps somewhat!
PS. If you are confused/stuck on something on your passport just give Equine Canada a call. In my experiences, they have been extremely prompt and helpful!