I had a feeling that it was a larger mirror than you first stated...
Your glue dots are only there to support the mirror in its packaging...not on your wall.
One thing I would do with an Ikea mirror before hanging it, is cover the rear of the mirror with gaffa tape or some other tape...because if some leans on it..chunks of glass falling are dangerous.
The mirrors I have fitted from ikea have all come with those clips and they are included for mounting purposes...if you follow the instructions, it's a fairly simple operation.
But if you start thinking about no nails...you will have fun removing it should you decice to decorate...keep a first aid kit handy.
Using the pads...for safetys sake use more pads than are required...peel one side of the pads and stick them to the mirror...then tape around the pads with the gaffa tape.
Decide what level you want the mirror...
Stick some masking tape to your wall at the height you want the bottom edge of your mirror to rest on.
Draw a level line across the tape using a spirit level.
Then peel the remaining sticky backs from the pads and offer your mirror up to the level line...make sure you get it right first time.
Apply pressure on the mirror, all over the areas where the pads were applied using a duster or a cloth.
Remove the masking tape from the wall...stand back and smile..