No, your dogs cannot mate without you being a breeder because by definition you intentionally mating them MAKES you a breeder. What quality of breeder a person is depends on a lot of factors however.
From another thread:
You don't continue the lineage of a dog just because you love them OR because they are themselves healthy and happy. It isn't about just that. There is SO much more.
You need to know the ins and outs of their genetic history to truly find out if they are of breeding quality. The histories of their dams/sires, grand dams/grand sires, and ALL of their litters, etc. should be known. Testing should be done to rule out genetic health issues.
Do you have that kind of history and research done even though your girl was abandoned? How much information do you really have on her history?
In addition, I have read that you do not truly know if they are of breeding quality until 2 years of age because there are some health problems that do not show until they are older.
I am not a breeder, but through just reading I have found out this basic information and more! I will never understand why people just stick their dogs together and THEN come doing research. This is something people should consider BEFORE breeding. Not after. There is no excuse for not doing research beforehand, especially if it isn't an accidental tie.

