Ruth, I recently tiled a bathroom myself. You can do it. Remove the toilet and tile around the hole in the floor. If you choose to leave the toilet and tile around it, what happens if the toilet cracks in the future and you buy a toilet with a smaller base, now you will see where the tile was cut!!
Something I wish I knew before I did the project:
When you add the mortar for the subfloor, the suubfloor, then the tile, you add height to the floor. When you go to reinstall the toilet, the water lines and the flange screws will not fit back in. You will need to buy longer screws and water lines. I hoped that will save you a an extra trip to the hardware store!!