In theory, the changeling is copying your actual appearance, including scars and the such. They don't copy your equipment or clothing.
In practice, the hair color and skin color (and sometimes gender) is often wrong, since the engine made these difficult to change. This may make it difficult for a changeling to copy your appearance exactly, because they shouldn't look different then you and run around claiming "I am this person; react as if I am!"
I suppose if you wanted a changeling to look like you, you could offer them your clothing and they could pretend to be you for a while, and it might be convincing with the same clothes/equipment, and if they had the same hair/skin color. (They could also purchase or obtain copies of the stuff you wear, though that may be difficult in the case of unique or hard to find items.)
The best place to go for answers like this, however, is the avlis boards-- changelings aren't actually a Ysgardian race and Avlis has the final say on them.
not an expert here, but i've always RP'd it that coran cant (or wont) copy someone exsact, that she can just learn a base form from someone aka human/halfling etc. If not then the addition that allowes a changling to cycle thru different head models also would make it too easy for a changling to cheese someone appearance without even knowing/studied them IC