That's a nice little plant.
Looks very healthy. Actually, it looks like you have 2 or 3 flytraps in there. I think I see more than one growth point.
No, don't repot now. Repot in Spring into a new medium (if you get a new pot, plastic or the like only - ceramic leeches minerals into the soil that can harm your plant - frankly the pot it came in is perfect).
Those aren't roots coming out of the bottom - it's long-fibered sphagnum (which is currently its soil medium). When you repot you can use 50/50 peat/perlite or something similar.
Take off that plastic thing. Most common misconception about flytraps is that they need humidity - people grow them fine outdoors in Arizona and New Mexico, where humidity is often under 20%.
Put the plastic pot in a real water tray (I've attached an example) about 1" deep.
Use distilled, RO, or rain water to water it - and only water the tray when the tray dries up completely (but don't let the soil dry out). Overwatering is bad (leads to root rot), especially since it's living in long-fibered sphagnum which retains water like crazy.
What kind of light does it get?
It also needs to go dormant for winter. Do you have a plan for dormancy yet?