Actually, there are no true allergy free dogs. Some (like poodles, for instance) are very low on the allergy scale, but some folks who are highly sensitive could still have a reaction to them. So just be aware that you could have a reaction to any dog of any breed.
Also, I'm a dog behaviorist and many of my clients are folks who meant well when they got their dogs, but chose a breed based on only one or two criteria and then were unpleasantly surprised to find they had a dog that didn't suit them in other important ways. So I would like to suggest that once you narrow your choices down to breeds that are low on the allergen scale, begin your research into each of those breeds.
The best way to do is to make a list with three columns. The first is what you must have in a dog. The second is things you could live with if you had to and the third is what you cannot have in a dog. So, if you are a very laid-back person, your first column might have "must be a quiet, low key dog". This rules out almost all terriers right there. If on the other hand you love to go, go, go and want a dog right beside you all the way, then terriers are a great choice for you.
Along those lines, I saw someone suggest a labradoodle a few posts back. These are great dogs IF you love a dog that is a challenge. These are two highly energetic, intelligent breeds put together. They have energy to spare, need tons of interaction, training and exercise to keep them happy and out of mischief. For some, these dogs are perfection, for others, they would be a nightmare. (A fair portion of my clients are those who chose a designer breed - which is a two breed dog, like labradoodles, schnoodles, goldendoodles, etc.). They failed to take into consideration the traits of BOTH breeds when they chose their puppy and then become overwhelmed as the pup grew and became too much for them.
I wish you all the best as you decide on your new furry addition. Just please do your homework and make sure it's not just a low allergy dog, but also a breed that you will love and cherish for all its qualities and characteristics for many years to come.