Well i can only tell you what we did last summer. We left Port Yasmine Hammamet Tunisia and sailed to Sardinia, over to Rome, down to Messina Straits, across to Albania, up to Montenegro and on to Croatia, over to Venice, down the eastern Italian coast to Sciliy and over to Malta and back to Tunisia via Lampedusa and it took 6 months.
If all you are going to do is sail and see nothing then depends on weather and miles you can make a day. If you want to see things then it will take a while. You can probably only really be underway from May to Oct.
What do you want to do? That is the real question? If you want to experience the Med it will take more than a couple of months. We are in year 3.
By the way this coming summer we are leaving Tunisia and head to Sciliy, Albania, Greece and end up in Turkey for the winter.
And do not forget that there are 2 winds in the Med, too much and too little so you will be motoring a bit.