I just completed this mission and will share with you how to do it.
Step one (fleet and finance organization):
Decom your mining ship and scout, and put your Anor Dreadnaught, Battleship, and one Crusier in a fleet. Set your spending down to zero, and 'buy now' a transport ship. Set your surveyor to 'automate' (and hope it finds a lot of money)
Step two (setting out):
Now send your two fleets to as far right as they can go (don't worry about your other two Crusiers, they will be used as bartering chips). Once your Dreadnaught fleet reaches the far right, contact the Altarian Resistance, and offer to exchange one of your Crusier for one of their worlds (and some credits if they will allow). The planet I obtained was Irug 'I. Estaenp'n is also a good choice. Now you should have two zones of 'life support' on the map. Your fleets can now travel the dead zone between them.
Step three (getting to the right):
Hopefully your funds will hold out (but if they aren't doing so well, don't worry too much). Send your Dreagnaught fleet over to the right, and after it's near the upper boarder where Irug 'I will let you venture, offer to trade your other Crusier to the Altarian for another planet. Aw'ess'il is one of the best to choose, though Ar'ther isn't bad either. This system will put you two systems over from where Du'toth is located. Once my transport / colony fleet got close, I sent the colony ship to colonize Ing'inay, which is probably the closest planet next to Du'toth. It was still uncolonized when I found it.
Step four (fight):
Now that you're here, the only thing left to do is to attack Du'toth with your Dreadnaught fleet to remove the ships, and send in your one measly transport to conquer the world. They only had 87 defenders vs. my 1000 attackers. I had 470 remaning but I won the fight, and the mission was over.
Note:
Don't confuse Du'toth with Dut'oth - they are two separate worlds, and Dut'oth is more to the left than Du'toth is. First time throgh, I found Dut'oth and thought, "Hey that's it!" but no, it isn't.