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Pets will only teleport to you when the chunk they are in is loaded. See the wiki page for more information.
As SF said, the fastest way is probably the nether; there are plenty of online guides on how to move pets through it. See this answer on viable ways to transport a wolf via water.
How Far Can Minecraft Pets Teleport?
Movement. When near their owner, standing tamed wolves wander randomly, but follow if more than 10 blocks away, and if more than 12 blocks away, they can be teleported to a nearby free block.
Dogs can teleport in Minecraft. Now my friend and I have built a new base thousands or even millions of blocks away from the old one and unfortunately we ate the dogs and cats there. If I teleport myself there now, free the dogs and cats and let them get up, can they teleport over this great distance or do they only have a certain range? And if I leash a cat and then teleport, will the cat be teleported with me?
How far will Minecraft dogs teleport?
How Far Can cats teleport to you in Minecraft?
Do pets teleport Minecraft?
Will cats teleport to you in Minecraft If you teleport?