Don't push yourself if you don't feel ready. That said, just be easy on yourself... instead of a Big Day Out, just a small first few things will easily suffice.
My first time out in girl mode early last year was going to be a trip to my gender counsellor, which involved a walk to the train station, catching two trains and a walk to the GC. I was pretty nervous, but the night before I had to take out the garbage...so I did that in girl mode. I realised the biggest fear was the first step beyond the doorway. Every subsequent step got easier. The next day, the fear of stepping out the door was significantly reduced. Yes, I ended up having quite a successful outing, but it had numerous challenges on the way - none of them went pear shaped but if they had... yikes. In retrospect it was a massive leap of lunacy but it smashed through a lot of fear barriers.
My advice to people is to take their first time easy, small trips, make sure you are able to extract yourself in (the unlikely) case of trouble. Day time is best, safe public spaces, some minimal human interaction, no alcohol, avoid overly crowded spaces with lots of random people. If all you do i s walk around the block, or jump in your car and go to the mall and buy a coffee then go home them you have covered a lot of ground.