Disclaimer: I have never used the original GalCiv II engine. I played the campaign in the Twilight engine. "An Unexpected Visitor" was the first map I ever played.
I took your 'single planet' statement a bit too literally, so I had assumed you had wasted your colony ship. Personally I colonized just like you and wondered basically the same thing. I took the time to power through select parts of the limited tech tree and figure out the game a bit before trading some of those advances for a much closer planet and some attack ships. At that point, death came pretty swiftly for the Drengin. I achieved military victory about 18 months in.
You should try to avoid feeding the Drengin your weaker ships, as it only makes them stronger through experience. Instead, pay close attention to the attack and hp of their ships. Ignore defense for the most part as only the floored square root of armor counts in its roll against beam attacks, ie armor 8 would still only roll between 0 and 2 when defending. Note that no other attack/defense types are available at the start of the campaign.
Make liberal use of tech trading with the Altarians to gain everything they research. Use spies or abuse the tech trading with the Drengin to see what advances they have over you. Better weapons and miniaturization let you build more powerful attack ships. I vanilla GalCiv favors bigger fleets (research logistics) over bigger ships since each ship can only kill one ship per turn.
Use
Kryo's FleetSim to get a better idea of what types of ships/fleets would bring down the Drengin.
Here's a few (hopefully helpful) things you may not be aware of:
1) You can buy ships/buildings. The ship/building is available the next turn regardless of the planet's production capabilities. Leasing is generally a rip-off, but on tiny maps you can likely lease fleets without any fear of ever having to pay them off. You can buy anything regardless of cost as long as you have at least 1 bc. Be careful though, as all production immediately ceases when your treasury has less than -500 bc.
2) The sliders are a rip-off. If you have the production slider set to less than 100% you're still paying full maintenance. If research isn't set at 100%, you're wasting maintenance on research buildings. If research isn't set to 0%, ie 1%/99% military/social, you're wasting maintenance on factories. If you play with any of these settings, you will likely need to pay attention to each planet's focus, as it converts 25% of all production points (before bonuses) to the focused area.
3) At 100% morale, your population growth is doubled. This allows colonies with 100% morale to grow exponentially faster than lower morale colonies. A small loss of bc in the short term can provide substantial rewards when you jack up the tax rate later.
4) If you're bored, build starbases. Keep sending a never ending stream of constructors to upgrade them.
5) Your starting colony ship is better than what you can create at first. You may want to use it to establish a colony further away from your home planet. You also want to land it on your starting planet and relaunch it at full capacity. Even if someone else colonizes the planet close to you, it will likely culture flip and get added to your empire along with free population and planetary improvements. This is less true on small/crowded maps, where the other civ has few planets.
Check out the
wiki for vast amounts of info and use these forums to check out strategies from players far better than me, like pretty much everyone over at the
Year Zero Club.