Yes, you can do this on your own.
You know it's kind of funny that you ask about fatherly types worrying. I tour solo. I love touring solo. I have a fatherly type who worries. I also have adult kids who worry. I still go. I'm cognizant of the fact that I'm traveling solo, and as valleygrl says...I keep my radar tuned. I'm a shortass...less that 5', so in my father's mind, that spells victim. Add the fact that I travel by bicycle, and it even makes it more of a worry.
I'm going to preface my next comments by...I'm 47 years old, have 2 grown children, and 4 grandchildren, and live at a minumum 6 hours away from all of them. Yet, when I tour, I give my children and my father some semblance of my route. Simply to give them a tiny bit of peace of mind, which gives me peace of mind. Last year I bought a $200 laptop, and journaled the trip that worried them the most. That way, they could travel with me. In my journal, I never said where I was going next...only where I was last. My family knew where next was going next. They also knew that I was safe, knew when I was struggling, and knew about the amazing people that I met along the way, and knew why I loved touring.
As you go along...listen to your gut. Always. Never ever question your gut. When there's a little twinge that something may not be right...assume that something isn't right, and move on. In all honesty, my gut hasn't spoken very often, and when it has...I listened. Through life, I've learned that my gut usually knows what it's talking about...whether I'm on a bike or not.
Ride...have a blast. Your father may worry...but he'll get used to it. Kinda. If you wait to do something that you really want to do, because you are trying to find someone who wants to do it as well...you may miss out on a lot of the wonders that life has to offer.
A few years ago, I decided that I wanted to do a triathlon. My dad came to visit while I was in the midst of training for it. When I told him what I was planning on doing, he said, "Why don't you go on a big bike tour instead?" In my dad's mind, the triathlon was even worse than a tour. We'll never know what worries our parents. As a parent, I truly don't know what my kids will do to worry me.
Ride...enjoy every second.