Minecraft – create another portal home from the end after I’ve lost mine

The dragon egg does absolutely nothing (well, apart from eluding most attempts to pick it up). Put it on your mantelpiece to show them online.

From Minecraft Wiki

To obtain the dragon egg, the player may push it with a piston, detonate it with TNT, or place a torch or slab under the block the egg rests on and then destroy that block so the egg falls onto it. It is possible for the player to hit one while it is still moving to the point it breaks, however this is difficult. Another solution, is that you can start breaking a coinciding block and then scroll over to the egg while holding the break button, in this case you will start breaking the egg instead of it teleporting on contact.

The end portal is positioned to try and trick you. Sometimes the portal may not even be attached to the main part of the stronghold. You could use xray or mcedit to find it.