Notice players in your guild aren't online as much as they used to be? Notice raids are more and more canceled and progress isn't going smooth anymore? That's all because of the end of Cataclysm. Patch 4.3 was the last World of WarCraft: Cataclysm patch, and Dragon Soul was the last raid with of course Deathwing as the final boss.

Because Mists of Pandaria is coming "Soon", a lot of players decided to stop playing WoW for a while. This happened with Wrath > Cata too, and will happen in the future with Mists > ??. When Patch 5.0 hits live servers, I expect to see lots of people returning to WoW. Another factor with the declining people online, is the release of Diablo III. In my old alliance guild, a lot of players were waiting for Diablo and are now playing it. Even my own friends, who used to only play WoW, are fully Diablo addicted and aren't coming back to WoW untill Mists.

Because of these two reasons I do not suggest transferring a toon to another server with more players at this moment in patch 4.3. If you're planning on transferring a toon in MoP, then sure.. why would you wait? But you shouldn't change servers when your guild isn't bussy or your progress falls behind. Give it two/three more months untill MoP hits. Then, reconsider transferring your character(s).

What to do untill then?

1. Level another toon. I almost finished leveling my paladin, and after that I'm planning on continuing with my warlock. Leveling can be done alone, and doing quests/dungeons rewards gold. 
2. Make a character on another type of server. If your main server is full, and it's f.e. a PvE server, you might want to think about creating a character on for example a PvP server. This way, you can A) look how such a server is different from yours and B) start all over again! No heirlooms, no gold.. no nothing. For some a dream, for others a nightmare but definitely timefilling untill MoP.
3. Change your main spec on one of your characters. I did this with my druid. I started collecting Agi gear with HP, and tried some BG's as Feral kitty. This was very challenging, because I had to learn a new spec, rotation and gear optimization. 
4. Solo old content, for gold and achievements/mounts or for Transmogrification gear. 
5. Do daily quests, for gold and reputation. This is really a time killer.
6. Plan ahead for Mists of Pandaria. What character are you going to level first? Are you capping HP/JP before Patch 5.0? Are you going to level a pandarian? Remember, you can have 11 characters in MoP so don't delete a character!
7. Try another game untill MoP if WoW is really boring. I recommend trying Diablo III, Rift and StarCraft II.