Correct! Only a small correction regarding the orthography: It's written as وقد and not و قد.
وقد is also very commonly used (especially in literature: novels, stories etc.) to describe a status, collocating with the past verb بدا (seemed, looked):
قال وقد بدا عليه الأسى: لقد فقدنا صديقًا وأخًا اليوم ( "With grieve/sadness clear on his face he said: Today we lost a friend and and a brother")
دخل الغرفة وقد بدا عليه الخوف (He came in the room looking scared)
نهض وقد بدا عليه الغضب (He stood up looking angry)
It's also a very common structure where وقد comes with الآن. In this case, "now that.." would be a smoother and a more accurate translation:
الآن وقد اجتزت الاختبار أستطيع أن أنام ملء جفوني (Now that I have passed the exam, I can sleep like a log (sleep as much as I please and without worrying). نَاْمَ مِلْءَ جُفُوْنِهِ = to sleep like a log.
الآن وقد أخبرته بما يدور في بالي أشعر بالارتياح (Now that I told him what is going on in my mind, I feel relieved.)
ما هي الخطوة التالية، الآن وقد أُنْجَِزَتْ الخطوة الأولى؟ (What is the next step, now that the first step has been accomplished?)