You're up a creek, as Dorsett Golden is the only tree that will pollinate Anna, but cold affects them differently. About the only thing I can suggest is that you can take cuttings of dormant Dorsett Golden branches, bring them inside to force the blossoms and them put them in a bucket of water under the Anna tree. You'll have to mess with the timing of this of course, but is the only hope you may have.

When I lived in Long Beach, CA, the Dorsett worked well. But the Anna could also set fruit without Dorsett's help. One can differentiate the unpollinated apples by their somewhat more elongated shape.

In that region, Ein Shemer was also a fine companion for Anna.

Beyond that, overly anxious gardeners stress young trees inadvertently by demanding it flower and set fruit in the first 3 to 4 years. It's far better to help the tree establish a sturdy root system prior to allowing any fruit to set and mature.

Because all 3 trees are so-called lo-chill fruits, I wonder if your problem is environmental -- that is, temperature.

Anna is self-fruitful. I have heard applenut say that they grow larger fruit if cross pollinated by Dorsett Golden or Einshemer. However they should set fruit even if its your only apple tree. My Anna flowered profusely this year and has set fruit even though none of my other apple trees have broken dormancy yet and its only 2 years old on a Full Standard rootstock.

If its old enough to flower it should be able to set some fruit. Assuming you have bees around doing their job it could be other things. Water stress could cause it to abort the fruit so could fertilizing to much at the wrong time. It could even be a pest issue but one thing it is not. It is not because its not being cross pollinated.

Does either the DG or Anna receive more shade than the other? (From nearby trees or buildings)

I've noticed differing bloom times in some of my fruit trees that should bloom at the same time due to differing amounts of shade from a neighboring two story apartment building.

Applenut had a post awhile back with pictures that showed differing fruit set on the same apple tree due to part of the tree receiving more shade than the other part due to an adjacent fence.