The following is courtesy of Rutland Manor, Australia

Because there has been no scientific study done to date on dog coats ( hair, fur ) and their relationship to allergies and asthma in human beings, the research undertaken by Rutland Manor Breeding & Research Center has been anecdotal. It has spanned almost eighteen years and has involved several thousand Labradoodles and their families.
Are all Labradoodles Non Shedding and/or Allergy Friendly? NO Are all Labradoodles free from doggy odor?    NO Are all F1B's (lab/poodle bred back to poodle) Non Shedding and/or Allergy friendly ? NO   Are all multi generational Astralian Labradoodles non shedding and Allergy Friendly ?     NO Why Not?   By the year 2000 the two founding breeders, Tegan park and Rutland Manor had established  most of their lines with non shedding and reliably allergy friendly dogs. By 2003 there were so many new breeders playing with this still developing new  breed, that all control was lost.  Even the term 'multi generation' lost its meaning, leaving a confused public who had no idea of what to believe  or disregard, with the differing information  given on  breeders' websites.  Almost overnight,  new breeders were 'experts'.  All their dogs  lived inside the house, all the puppies  grew up inside their homes, and  ( in print ) many  had mysteriously been breeding for years, whether or not this was actually true.  Worse, most  had no idea of how to tell the coats on their  puppies, and so, many 'non shedding' and 'allergy friendly' puppies went to unsuspecting families with the resulting disappointments seen all too often.  Breeding the amazingly popular Labradoodle was seen by many as a way to make some quick and easy money.  And if you gained a spot on the committee of one of the new Associations, well, that was the icing on the cake as far as credibility went!
Take a look at www.RutlandManor.com for more information.  Beverley Manners has wonderful training and information on her site.                  The following is courtesy of Rutland Manor, Australia
Experience comes with a price tag of multiple years of learning, and trial and error.   Hopefully the following will provide a guide to what you can expect from the variety of coat types being bred by many breeders. The Evolution of the Labradoodle Coat F1 (Labrador bred to Poodle) ....   This is 'Sunny' F1 as an 8 wks old puppy and at 18 mths.  Sunny starred in the Stage Production 'Annie' in Australia  in approximately 1995.  He was a short hair coat. Litter of 9 F1 puppies bred as potential Guide Dogs in the Czec Republic. The whole litter had Labrador type short hair coats F1 Silver Standard     F1 Silver Standard                        First Generation Lab/Poodle puppy and Adult   Hair (short) Coat multi generational adult  Shed heavily  Later generation long Hair Coat - beautiful but moderately shedding.  Best Coated (Hair Coat) around 1995. Lightly shedding     Wool Coat Non Shedding around 1995 Mutation Coat - starts off as fluffy puppy then coat drops out at around six months old. Multi Generation Flat Coat. Beautiful and low maintenance but sheds lightly Another Hair Coat. 2 Fleece, 1 Wool Coat 2006. Non Shedding Group of Fleece Coated Adults  Non Shedding Hair Coat  Will Shed Heavily This was the coat on a puppy sold by an American breeder to an unsuspecting family in South Carolina as a 'multi generation non shedding fleece coat'   "Fluffy" coat on early generation or badly bred multi generation puppy.  Beware, it will shed heavily  Another view of the hair coat puppy above The Wool coat grows out from the body getting thicker all the time.   It is currently the 'safest' coat for allergies and asthma but it needs regular thorough brushing, and trimming or clipping two to three times per year. .     Close up of Black Fleece Coat Spiral Fleece Coat.  Once this coat is clipped with electric clippers it will go curly and require regular clipping.   The true Fleece coat is an even length over legs and body.  Notice how the Fleece Coat flows freely in long tendrils from the body and legs in contrast to the Wool coat, which  stands  out from the body in tight curls. The true Fleece Coat from well bred dogs is non shedding and almost as reliably allergy friendly as the Wool Coat The pictures above are a Curly or Spiral Fleece.  If clipped with electric clippers these coats will go quite curly and some may never attain their former length due to the tightness of the curl. Above - Spiral Fleece Coat WAVY Fleece Coat Above.  The micron of the tendrils is wider in diameter and the curl is looser being wavy rather than curly.      The picture above  is interesting because it shows where the matting first starts during the change of puppy coat to adult coat which commences any time between ten and fourteen months of age and can last for a couple of months.  As the coat is non shedding, the puppy coat needs to be stripped out to prevent it tangling in with the new growing adult coat and forming matts. When you enlarge the thumbnail see how the matts are starting close to the skin and how they are being hidden by the long tendrils flowing down over them.   They are often missed as the long tendrils can hide what is happening underneath. The following is courtesy of Rutland Manor, Australia