Don't expect any issues going through security, but be prepared to keep the queue moving.
Here's my routine for going solo through airport security:
Bin #1: shoes & jacket
Bin #2: purse and anything else small
Bin #3: laptop
Dish: 3-1-1 bag
Carry-on bag.
And don't allow anyone to place anything between your items--including the TSA agents! I almost missed a flight because one of the agents did that and they held up the other passenger's bag for quite a while in the scanner. Be polite, but firm.
The method to my scanning order:
Shoes and jacket are replaceable. Not easily, but can be done.
Purse (backpack, whatever you carry) is critical. I want it to emerge from the scanner about the time I'm finished going through the metal detector. I keep my eyes on it at all times! Ditto for the laptop.
Carry-on bag brings up the rear. It's harder for someone to reach around it to get at the laptop. It's a 16" rolling duffel--holds my laptop, jacket and just the right amount of stuff to get me through a day or two if my luggage doesn't arrive at my destination when I do.
If you're searched (wanded, usually) by security, ask to be able to keep your purse and other valuables in sight or ask if they will bring them to you. Ask very politely. I've had a male agent be snotty about it, but when I explained I don't have pockets and my wallet, ID and everything is in my purse and I would be in serious trouble without it, he agreed to allow me to keep it in view. Fortunately, most of the female agents understand the predicament.
You most likely won't be stopped by the TSA for additional screening. If you are, don't take it personally. I seem to go through streaks--several flights I sail through, then I'm stopped for some reason or another on several flights. No idea why.
And if you wear any large jewelry or hair stuff (barrettes, etc.), be sure to remove them and put them in one of your bags before going through security.
You're going to have a wonderful solo holiday at WDW! I was mistaken for a teenager long--and I do mean long!--after I became an adult because of my appearance. Just follow the same rules you would at home for safety and you'll be good to go on the road!