If there is even a time limit it's most likely 6 months from the date of purchase but i doubt it.
You are free to still use your character. Transfers happen during server save. If you decide to transfer your chars just travel to Travora (The world transfer island) and talk to the npc on that island. He will tell you everything you need to prepare in order to transfer to your new home.
There are some restrictions.
1) You can't be red or blackskull
2) You can't be the leader of a guild. Leave the guild and/or pass the leadership before you transfer.
3) Remove all open buy and sell offers from the market. I think this happens automatically by now but just do it.
4) You can't be the owner of a house or a guildhall. Move it to a second character, sell it or just give it up.
Once the NPC tells you that you are ready to go and you actually want to leave your server ask the npc to teleport you to the transfer platform. If you character is located there upon server save you will be on your new server afterwards.