Your design is a common form known as a “writing desk” or a “library table”. Pinterest gets a bad rap in some circles, but I find it very useful for collecting ideas when I’m designing a new build. Search for writing desks and library tables in Pinterest and collect those that interest you and study them. Visit a furniture store or an antique store and take a tape measure with you. There are standard dimensions for these forms. You will find that the desk surface is typically 29"-30" off the floor. The apron is 4-5". Sit in a chair and measure how high the top of your thighs are off the floor and see if the standard dimensions fit you. You can vary the form and size of your desk however you like, but I think you will find that it is not necessary to reinvent the wheel. Just create a variation of it that suits your tastes.
After re-reading your initial post and seeing this picture, I think you were on the right track to begin with. I think using dominos both for the apron (1,2,3) and for the stretchers (4,5) is the way to go. I think you were rightly confused when you tried to model the half laps in corner #3. Those overlapping half-laps were not going to work. (Not to overload you with choices, but you might also consider a combination of half-laps (1,2) and dominos (3) in the apron.)
Just out of curiosity, what kind of wood do you plan to build your desk from? In your original post, you said you expect to be working with 1-1/4" wood. Legs typically start out square (2"x2" or 3"x3"), with the two inside faces tapered. Your design only shows a taper in the side view.
If you’re looking to learn about furniture and what it looks like under the hood, my all time favorite book on the subject is Illustrated Cabinetmaking by Bill Hylton. The subtitle is “How to Design and Construct Furniture that Works.” It is a gold mine of information on everything from furniture styles to furniture joints and it contains exploded drawings for just about every furniture form you can think of. It is a fantastic book. I can’t recommend it enough.