ah yes how to dodge a pirate....
personally i never really tried it but there are a few things you can do.
1. first travel only in very safe systems, untill you can afford a larger ship or at least a fast ship. that way you can outrun them. larger ship will provide oyu more shields.
2. to dodge the rocket ECM should do the trick, but don't count on it too much...
3. most importantly save often. sometimes if you save&load or travel at certain time compression you actually wont see any pirates. i once had a problem when i already had a larger ship and was attacked by imperial destroyer who was armed with plasma accelerator. i couldnt' avoid it and it destroyed me the second i dropped out of time compression. the solution was to be in system and travel with low time compression. he was getting close to me on couple of occasions but i always fired at him the right time (backside cannons) and managed to damage him enough so he stopped pursuing me.
4. you can use planets sometimes as hiding spots or use to to slingshot arround them (some physics knowledge should do the trick).
More on how to equip the ship what to selects etc. see Tricks and tips:
http://homepages.ihug.co.nz/~kelpi/kelpie/
on bottom part of that website.