Not OP but my partner lived in Copenhagen for two years. As with all of Scandinavia fluency in English is very common, practically universal in cities so you can happily live there without speaking a word of the local language. Also unlike most of Europe it's a lot more acceptable to just assume English is spoken and lead with that rather than stumbling through in the native language to start with.

That said it's still polite to learn some basics, e.g. thank you to mix in. If you're planning on living there long term you will want to learn Danish for social purposes unless you're planning to mix exclusively with immigrant communities. It's a very international place so English can often be the default language that any given group will all speak.

Edit: oh and an interesting quirk English is often spoken with an American accent! I think because they watch a lot of American TV shows and movies.

4 years. My kids are fluent now because we threw them directly into Danish public school cold-turkey as it were. My wife has studied a bit and knows some. For my part, I've just been too busy with work to learn much Danish and 99% of work is in English across a few organizations I've been with while being here. And 100% of the people you meet in Copenhagen will speak English near fluently so it is not necessary for daily life. In fact, you are more likely to find restaurants where nobody speaks Danish in the city. All of this is different if you travel to rural areas of course. It only becomes a problem if you are in a social situation with a bunch of Danes because they'll want to socialize in Danish. In small groups it is fine, they'll switch to English for me, but a big group makes it harder.

I moved to Copenhagen a couple of years ago. Still learning Danish but you can get by with knowing only English without any problem. Pretty much everyone can understand you.