It has been a little while since I ordered from them, but on average, it seemed to be right around 3 months when I ordered from MintonCard. I ordered three different dolls and a body over several years, they were pretty consistent. You might want to check out the IslandDoll waiting room for a better idea. If you order through a dealer, it may take longer than ordering straight from the company. Dealers usually submit a group order, so there may be a waiting time between when you order through the dealer and when they submit it to the company; plus the company then has to make multiple dolls before shipping any back to the dealer....then the time it takes to get from company to dealer who will check it in and make sure everything is right, then ship to you. However, shipping costs from a dealer may be lower than shipping straight from the company, and if anything does go wrong, the dealer will handle it for you. (For example, my Louis arrived to MoC with a broken hand, but they contacted IslandDoll and got a new hand sent to me pretty quickly, and I didn't have to do a single thing.)
There is nothing in the waiting room. Don't bother to look. I went to check for myself a few days ago, and it had not been updated for months. I just started a new list. Hopefully, someone else will chime in. Thanks, @CloakedSchemer, for your info!
My first two Island doll Bru were quick to arrive, purchased from Alicescollections. Waiting on the third...been about 4 weeks now.