The covering letter sounds very good. There's just a couple of things I'd do to improve it:
1. Don't mention that you don't have a university teaching degree. If they specifically need you to have one they'll say and anyway it should be on your CV if you do. The main reason for me saying that is that I've always been told that you should emphasise the positive and not the negative. Especially with it being so early in the letter, they could just read the fact that you don't have it & stop reading there. If you are studying for it, just say that. Try to avoid using negatives.
2. Instead of the sentence starting "I am, herewith, enclosing..." I'd just say "I enclose my CV and hope to hear from you."
Hope this helps and good luck!
- For Teachers