Once recall is firmly established, there is no reason to wear yourself out over the DJ. You can jot bullet point or use a voice recorder, or you can just rehearse the dream mentally. Be warned--you'll lose some details this way.

DJ is most important for establishing recall, finding dream signs, and keeping an eye on your overall practice (are you noticing odd things in dreams? Are you discussing dreams with DCs? And so on). It's good to check in every once in a while, as dream signs can change.

Sounds like a really promising start. Those awakenings are excellent for promoting lucidity.