My Take:
1. Queen hitchs a ride on the dropship - she has a facehugger with her at the time that came with her from the nest. This is a normal facehugger.
2. Queen lays an egg on the dropship en route to the sulaco.
3. During the fight between Ripley and the Queen, the face hugger drags the egg away through instinct "don't be where your enemies expect you to be"
4. After they are in hypersleep, the egg hatchs and we now have two facehuggers. One attempts to get Newt and fails cutting itself on the glass causing it to bleed and cause the fire. The other (the one just hatched) gets Ripley.
5. After they crash land, the other facehugger then gets the dog.
A super facehugger can account for the two aliens (getting Ripley and the dog) but a superface huger doesn't explain the location of the egg on the Sulaco.