Well, no air filter is not a good thing because even the smallest particles of dirt will get sucked into the carb and scratch the cylinder walls causing a loss in compression (over a long period of time).
The float in the carb could be stuck and the carb could be flooding over into the engine. This will give it too much gas and the engine usually will not idle and it will run like a dog. Smetimes a few gentle taps on the float bowl with a plastic handle screwdriver will get the float un-stuck (if it is stuck)
Make sure that you don't have the choke in the on position because that will give you the same symptoms.
If you have a muffler on your exhaust it is possible that it can get clogged up. But if the engine and exhaust are only a week or so old, a clogged muffler probably isn't the problem. It takes a long time for a muffler to clog up, but it can happen.
What is your fuel-oil ratio at right now? Sometimes if you have way too much oil in the gas you will have the same problem (low power and no idle). They say to run 16:1 for break in, but 20:1 is ok and the engine will run alot better than it will on 16:1. After break in you can go to 32:1, but it's all a matter of trial and error because some engines run good on 32:1 and some don't. Fuel-oil ratios can be a huge debate.
Another thing that can and has happened on some of these carbs is that the main jet can fall out and be laying in the bottom of the float bowl.
Pull the carb off, remove the float bowl, and see if the main jet is screwed into the carb or laying in the float bowl.
If you are running the orignal plug wire that came with the engine, go get an ngk B6HS plug and throw the original one away.
Do yourself a favor and go get an automotive style spark plug wire with a rubber boot and replace the stock one with it. (You will need the little cap that screws onto the top of the spark plug for an automotive type spark plug boot to snap onto the plug)
The stock wire will just unscrew fro the cdi box, and you can just screw the bare end of the new wire into it, centering the screw into the center of the wire so it touches the actual wire and not the outer insulation.
Check all of your wiring because if any bare wire is touching anything metal, you can lose power going to the cdi, resulting in a weak spark, low power and no idle. (or the engine will not run at all)
If you have something (like a headlight) hooked to the white wire, disconnect it.
Cut the bare end off of the white wire and cap it off. Having something hooked to the white wire will pull too much voltage from the magneto and give a very weak spark. Having a headlight hooked to the white wire may work for a day or 2, but eventually it will draw too much from the magneto, and the magneto will get weak.
If you used those cheap push together wire connectors, cut them off and solder all of your wire connections together then cover them with heat shrink (or black electrical tape at the least) and make sure that there are no bare wire touching anything.
There are a ton of variables to try and figure out what's wrong, and it will take awhiel to narrow the problem down.
More than likely, it's a simple fix.