I’m not familiar with おやすみプンプン, but I did just look up pictures of the manga. What stands out to me is the lack of furigana readings on the kanji.
The very first manga volume I ever read all the way through also did not have furigana. I bought it as an ebook, which let me use a computer program to convert the kanji from manga page images to computer text. With that, I could look up the reading and meaning. It was a very long process, and not one I’d recommend for most people.
The best question to consider is: how is your grammar? Have you started learning grammar yet? If so, how far have you gotten?
You may want to check out the Absolute Beginner Book Club. We’ve read a few manga (and some very simple children’s books), and there are discussion threads about the material: