I know it's probably not what you want to hear, but I would say wait a while before you go into a level 4. Here's why:
Your plan to use an Armageddon is fine, but frankly you need more skills. If you rush into level 4s you may just end up losing your BS. Your tanking skills need more development. Your weapon skills as well, because killing things fast becomes part of your tank at the level 4 stage.
I note that you are training trade 4 for some reason. If you want to run level 4s that skill will not help you. Start toward getting sentry drones, and tech II ones at that asap. Also, you need more drone support skill development. Read the descriptions of the skills on the market. You will figure it out. Also, don't neglect amarr drone spec, and even caldari. Ogre IIs, etc look great on paper but gallente drones are the slowest moving drones. Heavy drones in particular are agonizing slow for missions. The travel time on them is atrocious and if they are far from your ship they will get targeted and die. What you really want is Curator II sentry drones for amarr rats. Also Warden IIs are great if you get gurista rats.
Your general support skills also need more development. The two main cap skills you should put to 5, and you will want armor repair systems 5 and upgrades 5. Also, don't neglect navigation skills. Particularly evasive maneuvering. It will speed up your ability to align and warp out. You will probably need this when you start out.
Eventually you should also train Caldari BS. You already are investing in missile skills. Training Caldari will give you a Raven to fly a shield tank. There is no one ship that is the best for every mission in this game. Having two races of ships will allow you to use a more appropriate tool for each mission. Also later if you pvp you will have options with which to fit into any fleet. Lastly, training Caldari in addition to the Amarr ships will open Sansha ships to you.
It may seem like it will take forever to train more but it really isn't. However, with your current skills I think you would quite probably lose your BS very soon, and even if you don't you will probably take a long time with many warp outs in order to complete many level 4s. Give it another month. Look at where you are then and make a realistic decision.
My advice would be to wait at least a couple months but I understand the itch to move on from level 3. Try seeing how quickly you can complete familiar level 3s in your Proph in the meantime as a challenge. The gap between level 3s and level 4s is not a small one. Have some patience and you will enjoy the experience more. Good luck to you, when you do make the leap.
edit- I took another look at your skills. I see you already snagged Caldari BS. Great. Train both it and Amarr BS to 4 at least before you take either into a level 4. Again, your dps will be part of your tank.