All you would be doing is perpetuating the problem of backyard breeding and not breeding for the betterment of the breed.
I don't want to appear brutal but looking at the pics and from what you have said I would not breed from this girl. And in no way would CoL condone this type of breeding anyway. You would not find any owner of a quality stud to support your venture either.
But if you decide you want to go ahead there's nothing anyone can do to stop you but think about the potential cost and I'm not talking purely financial. You could lose your girl and or the puppies. Are you prepared for that?
I'm sorry you are likely to get a lot of negative responses. I would be shocked if anyone supported you in this potential venture. If you wish to become a breeder of cockers - fine - but please go about it the right way and that starts with doing an immense amount of research then finding a reputable breeder who can then mentor you through the process and ensure you have a girl that is suitable for breeding from and that you do know what you are doing.
We are actually wanting to keep one of her puppies as we thought this would be a nicer way for her to get to know a new dog instead of buying one
As it is, you say you simply want another cocker. That's understandable - but there are much better ways of going about that and that starts with finding yourself a reputable breeder.
It will also cost you a lot less than breeding your own girl - if you do it properly with her and the puppies wellbeings at heart.