Most anemones can tolerate a lower nitrate level just fine, and may even benefit from the DOC. It's more important to let your tank cycle and age before getting an anemone than to worry about a nitrate.
Anemones need high levels of dissolved O2, a salinity at 1.024 to 1.026, a stable pH between 8.1 and 8.3, temp between 76 and 78 F, calcium between 400 and 450, dKH at 8.0 to 10.0, magnesium between 1.250 and 1.350 ppm, Nitrate at 2 ppm to 4 ppm is best), stable phosphate at 0.002 ppm or less (0 is best), and finally 0 ppm of ammonia. Just as with most all aquatic life, stable parameters and parameters at or near the desired levels is the key to a healthy and happy tank with healthy and happy anemones.
One important thing to keep in mind is that it is best to maintain proper and balanced levels of Calcium, Alkalinity, and Magnesium in order to have a proper and stable pH. This will help to maintain levels close to that of natural sea water.
Anemones need at least some water flow around them. They breathe by absorbing oxygen directly from the water. In the wild, anemones also need water flow to bring food to them and for carrying away wastes. Generally speaking, anemones will need moderate to low water flow. One of the most common causes for an anemone not to be happy in your tank is that they do not like the water flow around them. This will sometimes cause them to move until they find a spot in the tank that they like.
Additionally, anemones need really good lighting to survive, similar levels to SPS corals. They will get a lot of their required nutrients through photosynthetic processes. They contain zooxanthellae algae within their tissues that will allow them to use light for nutrients.