Go to
http://www.caudata.org/cc/articles/cyclingEDK.shtml
You can cycle with your axie in the tank but you will need to test the water every day or two and do 20-30% water changes regularly to keep the levels within a safe range.
I assume as you have an undergravel filter that you have gravel on the bottom of your tank. Both those things are not a very good idea. Axies can swallow gravel and cause blockages that make them sick and I have heard many times on this site that undergravel filters are hard to work with and get gunk caught under them. Good alternative substrates are sand, nothing, slate slabs, or very large pebbles.
Could you post a pic of you axie? It might help people to identify what u r talking about.
Cycling refers to the nitrogen cycle. Axies produce ammonia as waste. The first stage of the cycle is the growth of bacteria in your filter and on surfaces that breaks down the ammonia into nitrite. The second stage is the growth of a second lot of bacteria to break down the nitrite into nitrate. If the tank isnt cycled you could get a build up of ammonia which will kill your axie.
If you are going to cycle with your axie in the tank then you will need test kits for ammonia, nitrite and nitrate ASAP! If you cant get them right now, either take a water sample to your local pet/aquarium store for testing every day or two and write down the numbers for those 3. The alternative is to put your axie into a tub with dechlorinated water and change the water every day or two till your tank is cycled.
When the tank is cycled, levels should be as follows: ammonia - 0, nitrite - 0, nitrate - 20 or below.
What type of filters do u have btw? How big is you tank?
Good luck!