Good instructions can be found here: How to repot a Venus fly trap
There is no need to keep any of the original soil with your new VFT. It will adjust just fine without it. The best way to transplant a VFT is to gently remove it from its pot. If the pot is really small, as in your case, you might have to "massage" the sides of the pot to release the roots from the pot. Once you have all of the soil out of the pot, gently break it way from the rhizome without breaking or tearing the roots. Finally, dunk the entire plant in distilled water to remove any soil left on the roots that wouldn't come off with gentle prying.
Then, in the new pot with the new soil, make a hole with one of your fingers. Try to get the roots in the hole without making them fold or wrap up (so you need to try to make the hole as deep as the roots are long). Cover the rhizome completely with soil by pushing the soil in from the sides around it. You should be good to go then.
I too bought some VFTs that came in really small pots last year. I repotted them about this time. Their growth stalled for a week or so, then they started putting out new growth. They made it through the winter fine and came back strong this spring. I am sure that yours will do the same. Good luck with the repotting!