Workout programs can always be improved. Don't worry if this isn't perfect.
This looks like a good plan to get acquainted. A standard approach would be to pick an off-the-rack program such as Starting Strength, Building the Gymnastic Body, Power to the People or similar, but if all you have is dumbbells then this is a good start.
Three sets of five is fine if you're going heavy. If 3x5 is too easy because the dumbbells are too light, either get heavier weights (perhaps a barbell) or do more reps per set. Pavel Tsatsouline's Enter the Kettlebell has some good methods for improving strength without changing the weight: ladders.
Pick a kettlebell you can clean and press--a clean before each press, that is--roughly five to eight times. C&P it once with your weaker arm, switch hands and put it up with your stronger arm. Rest. Two reps. Another short break. Three reps. Then start over at one. Do three ladders, for a total of 18 repetitions, the first week; add a ladder the next week and a ladder the week after. Five ladders, total 30 reps.... The fourth week keep the number of ladders at five, but now try to work up to 4 reps.
This "ladder" approach may help if you have a dumbbell that is challenging but not impossible for you.
But all of this doesn't matter. Training hard, training consistently, and eating well are what matter. If your workout is a doable challenge, in the grand scheme of things you're fine.
Ideally you'd start with a brief whole-body workout, like a jog, dynamic stretching, or joint rotations. The pushups and situps should be easy enough to count as warm-up. Over time, try to eliminate the break after them.
Another thing to consider is tacking a quick 5- or 10-minute all-out conditioning session at the end. Or you could do sprints, either in a separate workout or interspersed with the lifting. (Dan John, Robb Wolf and Greg Glassman are big on lift-plus-sprint couplet workouts.)
The primary problem with this plan is that the weight will very quickly stop being "heavy" to you. With even a couple weeks of training, most humans get very good at squatting and deadlifting much heavier weights than they can curl or press. It's likely that you'll stop challenging yourself on the lower-body exercises fairly quickly.
At that point, you'll probably want to research Pavel's material as noted above, or look into pistols (one-leg squats), jump squats, single-leg deadlifts, Romanian dumbbell deadlifts, and other ways of continuing to challenge your squat and "hinge" (deadlift) strength. Maybe you'll move to barbell, kettlebell, Olympic, or gymnastic work.