[pushkins]

No, No and No.
Never use MDF as a sub floor for tile...NEVER

First fix the creaks, you need to first screw down the existing floor to the floor joists, if you can see the nails in the existing floor then use these as a guide. Use screws NOT nails.

Then install 1/4" backer board, it's available at all big box hardware stores ( Lowes and Home Depot, approx. $10/ sheet 3x5) make sure you use the backer board screws with a square drive head ( $10 a box and 1 box does three sheets, they are green)
Make sure you screw the backerboard at all the indicated spots (it has small depressions where screws need to go)
The backerboard can be cut by scoring and breaking or if you have a masonary blade on your circular saw this will work well too.

For some added stability you can apply a (1/4" notched trowel) layer of tile thin set mortar under the backerboard directly on a clean sub floor, if you do it this way you can use 1 1/4" roofing nails instead of the backerboard screws.
Do not let the thin set applied under the backerboard dry before you nail or screw it down.
If you use thin set under the backerboard then let it dry 12 hours before tiling.

Good Luck