For your AMMs, the speed CAN be a problem. It's not likely.
If the enemy missiles are as fast as yours, with some luck you hit them, but if your missiles move first (it's turn based after all), then theirs, you end up behind the target and can't catch it.
However, it is very unlikely someone will build that fast missiles, at least 4 WH strength are a must to penetrate armor properly.
Most reasonably enemy missiles will be around 50k speed at those tech levels. I don't think you'll be running into a problem there, aside from the fact that a hit doesn't do anything, of course.
I'd recommend just increasing your missile to Size 3, and using reduced size launchers. Yes, they fire less quickly, but given enough range, Alpha Strike is all that counts. If you already built your ships, add a few WH 4 missiles with shorter range to punch the enemy if he comes close, that way you get the best of both worlds, if your economy is up to the task.
If an enemy has a ship like your carrier, with 10 levels or armor (Which is agreeably on the heavy side), that would be 610 points of armor total, and with the flat craters of wh2 missiles, you'll need a good 250 hits before you do any internal damage.
Now it happens that in all likelyhood your missiles are already roughly as expensive as the whole enemy ship, and if you have ships fireing those missiles, you might lack missiles in the end to kill everything. As such, try to get at least a single ship with heavy beam weapons to finish off enemy stragglers, just in case. It doesn't need to be particularly good, because if you ever happen to get into a knife fight, your dead anyways.
I would suggest going strongly with the fighters here, they pack a heavy punch, add decent range to your attack (at that tech level, a missile should itself have 100-150m range, with sensors way longer, as already said^^), and you can spread fire close to the target and thus evaluate the results more quickly. However, the maintenance on your Carrier is pathetic, that thing will break down before it reaches the combat zone, it's fuel it not really on the high side, and the magazine size needs an overhaul as well.
Keep in mind those Jump drives are of considerable size, which could just as well be invested in an additional level of armor, more speed, or shields, to prevent needing to retreat in the first place.