I think that it is well worth getting several tutors. I have about 10 that I accumulated and can particularly recommend these:
“The complete Irish tin whistle tutor” L E McCullough
“The Clarke tin whistle”
“A complete guide to learning the Irish tin whistle” Clare McKenna
“The essential guide to Irish flute and tin whistle” Grey Larsen
Like you I had the advantage of being able to read music and that will really speed things up for you. All of the above are available with CDs.
There are also some superb resources on the Internet that were listed in a recent post here.
I’m also a Dane who is all new to whistling. I’ve made noises on my whistle for a couple of weeks now. As for tutors I have bought “A complete guide to learning the Irish tin whistle” by Clare McKenna from the music room. I got the one with the included CD (it’s nice to hear how the whistling should sound like). IMHO it’s pretty good (but then again I have no experience to speak of)The URL of the music room is: http://www.themusicroom-online.co.uk/
I plan to buy others in the days to come. I think it’s nice with several tutors.
Apart from that there are several online resources. Check out this thread: http://chiffboard.mati.ca/viewtopic.php?t=46338 for the recommendations I got when I introduced myself. There’s enough out there to keep You busy for a while!