I think the main thing you need to do is decide how YOU want to move forward, what will make YOU more comfortable....it's not about what you therapist wants, for whatever reason. Yes, use them as a sounding board and take advice, but with the best will in the world, if they have limited experience of dealing with trans people and aren't trans themselves, then they aren't in any position to decide what is best for you.
They're right about the people around you accepting you, but in reality they either will or won't, however you approach it. Definitely let them know what is happening and be open to discussion with them about fears etc, but do what makes you feel good and comfortable in your own time, not someone else's and definitely don't hold yourself back because other people are having trouble getting their heads around things; how long has it taken you to get used to the idea of your gender? Do you really want to wait that long for others to get on board, and what if they never do?
Your life is for you to live, not for others to be prescriptive about how you should be. It's definitely difficult at times, and the hardest things are often the most rewarding and necessary, so decide what it is you want, make a plan to deal with getting yourself there and then do it for you, not for your therapist or anyone else. It's hard to tell from your post whether the psych is taking this approach because you're waiting for direction or whether they're actively trying to direct you off their own back. Neither is great though, take the reigns yourself, you'll feel better for it.
As for feeling generally feminine in yourself; I found that feeling came on over time once I started going full time and then more so when I started hormones. The reality is that you need the time to let your brain drop all of the male facades it's put up over time to try and fit in to society, which isn't instantaneous and, in my opinion, isn't going to happen if you hold back on moving yourself forward. It's like trying to get to the finishing line of a race but just sitting on the floor and doing the leg movements of a person running....looks similar, but is very unproductive.
In my experience, I found that doing the basic groundwork with those who are important to me and my workplace (letting them know what's going on, mainly) then just jumping right in got all of that terror out of the way in one go, leaving the bit following my 'official' move to presenting full time as the correct gender, going by my new name, etc, as an exciting adventure to enjoy with a few things here and there to mop up as they became apparent. I found this a much better approach than trying to guess all of the issues that may arise and then deal with them before they were an issue, which would be a waste of energy handling things that may never happen. For what it's worth, a lot of people may feel that they wouldn't be able to handle you in your new role, but when actually faced with the reality find that they're fine....making a big deal of it yourself makes others treat it as a big deal; act like it's normal (which it is, everyone else gets to wear whatever they want to feel comfortable!) and others will see things as normal.
Bottom line; do you want to wait to be yourself, or wouldn't you rather spend this time that you're looking at what you want to be actually properly exploring yourself than just imagining what might be when everything is in place and perfect for you to make the leap? Because, in reality, nothing is ever perfect and you'll be waiting forever if you take that approach.
