I think you should its great having the courage to play without a teacher. The first step you should do however is GET A TEACHER. The benefits are too numerous for me to list so I am going to go over and give you some suggestions
If your goal is to improvise you a have to make some goals of what kind of improve do you want to do? Classical improv or Jazz improv? Which ever one you choose you should start listening to that kind of improv. Remember Improve is not just playing scales and arpeggios. It requires first of all technique to play the instrument, a knowledge of musical patterns, and it helps to have a great ear and knoweledge of music theory. It would be wise to gain experience with technique, ear training and theory. If you want to do improv, you should start today and experimenting and playing around with the piano. From my personally experience me having a large background from sightreading pieces helped me be able to do classical improve fairly quickly. As far as practice heres a routine you could try
Warm-up-scales, Hanon- focusing on finger independence, dexterity, lack of tension, strengthening 4 th fingers and improving tone
Improv- using melodies based on keys learned in scales
Repertoire- practice enjoyable pieces that build technique, provide a challenge and improve reading
Sight- reading- playing pieces you are familiar with-preferably a big book of popular tunes- playing them once and only once, looking for familiar patterns, easy pieces quick, hard pieces
slow, observing at a glance key changes, time signatures, expression markings, titles, chord progressions
You should be capable of playing music without listening to a recording because there may come a day where you have to preform a work where there is no recording and you must learn it. You will eventually have to know what time signature and be able to play with a metronome. There may come a time when you will have to play with a band and everyone can keep the beat but you! The metronome will not lie. Remember just because the pieces is recognize able does not mean you are playing it in rhythm. I have had many students that they play and they are "in the area" of playing on the beat but they are dragging/ playing different tempos/ rushing many things that because obvious by using the metronome.