make sure the filter is for double the tank size, if you can increase the bio-media, make sure the water is adequately oxygenated.
an axolotl tank is normally bare bones (lacks substrate etc..), this means the filter has to do all the work (in effect it is cycling the filter)
bio-media is used to house the bacteria that consume/convert ammonia and nitrites, the more bio-media the larger the bacteria colony.
the bacteria that consume ammonia and nitrites are aerobic which means that they require oxygen to consume/convert ammonia and nitrites, this is why having air-stones in the tank are important, lack of oxygen can be harmful to the filtration as well as any tank inhabitant.
after a month of cycling the nitrate should be a lot higher, how are you cycling?