Basic answer, but here goes.
I bowhunt Jersey in a non-permit zone, during a non-permit season. So for me, I only need what you now have. It took me a while to understand this, even with an Uncle who lives there helping me out. You have to read the regs on the zone you are hunting for exact rules, but for me in Zone 21, it goes like this:
I get to take either sex, 2 deer per season (one of each). If I shoot a doe, I use the transport tag, go get it checked, and then get another transport tag. If I get a buck (3 points on one side for that zone), then I use the buck tag and the transport tag, then get another transport tag for my doe when I get the deer checked.
Remember, you have to get the deer checked at a station in New Jersey.
See this page of the NJDEP site for more detailed info: (PDF FILE)
http://www.state.nj.us/dep/fgw/pdf/2006/06-07deer_regs.pdf
This one has all the info you'll need:
http://www.state.nj.us/dep/fgw/njregs.htm#hunting
MAKE SURE you know where you are hunting and the particular regs for that zone. It various widely, and some zones are nothing like I just described to you.
If you check my site, I have a New Jersey section that a long-time Jersey hunter frequents. He has helped me in the past with questions. Give him a shot.
Good luck, Jersey has great hunting and cheap gas! That is why I originally switched. I live in NY, but closer to my hunting in NJ. I hunt in Double Trouble State Park in Ocean County.
Where are you planning on hunting? I might be able to help you more.