Is this the one with the Gigantic galaxy and you have to invade the itty bitty planet at the south corner?
I played this in pre-beta. Not sure how it works in 1.1--frankly, I think the DL campaign will need some re-balancing in 1.1. But what I did was first get Planetary Invasion, some engines, and some Basic Life Support as quickly as I could. There's not much time to crank up the economy first. Those transports (I suggest two of them, with 1 troop module apiece) have GOT to be on their way. It's a long trip, and you want them safely away from Earth before the DL's find you. The DL's are targetting Earth--not your transports--unless they're in the DL's sensor range, then you're screwed.
Next you need a couple constructors to extend your range. It doesn't hurt to research a little more Life Support after your transports are launched, either. You also need a few fighting ships to escort your transports. Nothing serious, just enough to take out the Defender(s) on the southern planet. I just sent in my Battle Axes, because I didn't know how hard it was going to be. Now I kind of wish I had left them to defend home.
Next you need some defense of Earth, since if it's invaded first, you lose. I played the usual DL defense I learned in the Siege mission: sensor ships (this is pre-beta), & cargo ships loaded with engines and 1 laser to take out the transports. I also built extra fast Survey ships, since there were plenty of anomalies to find, and they could always double as sensors. If I could get any of my ships to 11 speed or faster, I could usually bait away the DL's escorts. It's all really just a delay tactic--I don't really care about his escorts, I just don't want a transport slamming Earth before I get that planet to the south. The important thing is, the transports have to be in the air BEFORE you shore up your defenses. You have that quiet period at the beginning.