New to Traveller, New DM

Also, at law level 9, its possible even a diplo vest is against the law. Obviously a lot harder for law enforcement to see it, but if they pat you (customs at landing) down, it could get you in a lot of trouble.

A TL 9 world, with trade to surrounding systems, could still have TL10+ for sale, it would just be impoeted and possibly cost extra.
I think I've just set myself up for some hard times, unintentionally. As I said earlier, I don't have a jump drive, so I created an entire system. The highest tech level in the entire system also happens to just be 9. If I understand the rules, I shouldn't be able to acquire anything over TL9. This is where my frustration is coming from. I have two habitable worlds, and BOTH rolled out as a Law 9 and TL 9. I finally made the ref decision to let myself use my pinnace as a 25% down payment on a bigger ship with a jump drive. I created a 100-ton freighter (again, limiting it to TL9 to play within my established backstory and current location.) First hop, nearest system with better tech! I was dumbfounded that my two planets ended up being so similar. The only key difference is one is a religious dictator, the other is a representative democracy.
TL 9 is significantly better than Earth is currently and that shouldn't really cause any troubles, though TL 10 gives you very significant increases in the "my normal clothes offer protection" options (if you have the Central Supply Catalogue rules). You may also want to pick up Journal of the Mongoose 2e Traveller's Aid Society volume 12, which has those John Wick suits that give 3 armor at TL 7 and cost double what your clothes normally cost. (you can get 5 or 8 armor that is not obvious at higher than your current TL).

You can also just travel without having your own ship. Granted, bringing a ship's boat along is pretty expensive. But if you are bringing some cargo in that boat's cargo hold, that'll offset it somewhat. But, a 100t jump capable ship is generally more useful for play than a ship's boat unless you really want to develop that one system and the worlds in it. I've done that with some campaigns. That's what The Expanse is, after all. But it is not the usual way people play.

Regarding TL, that's telling you what is commonly available at the standard prices because it can be locally made or is imported in bulk. But you have interstellar trade. So better stuff can be available. It'll just be more expensive, may require an "adventure", or be a prototype (rules for that is in the Central Supply Catalogue).

You are trying to learn the rules and you are self DMing, so I understand wanting to be pretty literalist. But EVERYTHING in Traveller is fuzzy. Your world's population profile might only count the human colonists, not the native sophonts who hide in the outback. The atmosphere might be "tainted", which means a filter mask in the rules. Except this world's "taint" is unusually low oxygen content, so you need a respirator despite normal atmospheric density instead. The TL is 9, because the space tech is primitive and they hate computers, but man do they have fancy genetic engineering. Law level 9 might consider a fancy bullet resistant sports jacket to be "armor" or they might only consider flak jackets with hardened plates to be "armor". Or they might require expensive permits. Or it is okay for folks that are SOC 8+, but not for those with lower SOC.

Do not make the game unfun or limit your creativity by strict interpretation of the world building system.
Yup, this is definitely a system that benefits from 'yes and...'

Law level is high and prohibits things? Yes and... they have one weird exception. TL is low? Yes and... they have 1000 high tech ships passing through every day because its a perfect trade route with free refined fuel.

Always use the results to spark creativity and interesting scenarios.

That being said, i like your dagger v stunner scenario. I think you did that very well, and learning how dangerous combat is, helps a LOT for your overall game. I think you played it out beautifully.
Thanks everyone. It's so hard not to get wrapped up in the rules. Many Dms can be pretty hard nosed, and I'd prefer to be a bit more relaxed. The fuziness makes learning the core rules a bit of a challenge in areas, but today my son and I was able to spend 8 hours just diving in, and with his DM experience, we were able to make some significant progress on understanding the game. We did a kidnap rescue from some local thugs that with everything I've learned so far went flawlessly. We did some serious trading, and finished off the evening hunting down a smuggler ship and destroying it. With the story that was set up, it was an older ship with quirks and limited weaponry, but still had the potential to hurt us. They only hit us once, but that one hit did two criticals. Thankfully we had a pair of missile launchers and while it took a few turns, it was an exciting scene. Now I just need to figure out how to balance payouts, cause the repairs and refit far exceeded the money we made! Had we not been taking advantage of every available passenger and trading while searching for the smuggler, we would be sitting pretty bad for our next mortgage payment. I really enjoyed the game, but perhaps having my son's attention for a full 8 hours was definitely the highlight of my day.

Getting your ship shot up is definitely a potential disaster! Or the set up for taking one of those high paying jobs you'd really rather not do!