Really considering moving to Copenhagen

Currently living in Australia and studying the options of taking this job offer. I've read about the high cost of living there and would like some information. The most important thing is to find a place to rent Protected content house or townhouse with a garden for our Husky. I'm sure is going to be outside the City because the high prices right? Hubby will be working downtown and we want easy commute by metro-train-etc? We don't want to live too far away and at the most will be half and hour. Any ideas about little towns or suburbs around with easy commute to look for? Is it hard to find a place to rent with a dog? Any information will be appreciated! Cheers :-)
Claudia