"Is it raining?"
No. Consider this: What is doing the raining? The weather is, and that's called "vejret" in Danish, so you need to say "det".
"Regner den?" is a valid and meaningful Danish sentence, but it would mean something else. "At regne" can also mean "to calculate". It would be a valid question to ask if e.g. "den" refers to "computeren" (the computer).