This Burpee-Row combo answers an oft unasked question: Yes, you really can add a burpee to almost any exercise. Burpees are to exercise like black pepper is to food - Sprinkle it into your workouts and you get a little extra kick.
Now, because of the added movement of the burpee and the fact that you're holding weights as you stand up and squat down, you really need to watch your back here. As you squat down and stand up, make sure you stay in a low squat with the hips back and down, the back straight, shoulders back and abs engaged. Keep the move slow and controlled, rather than using momentum. If your back or shoulders are rounding forward, keep the weights on the floor throughout the exercise or switch to very light weights to practice good form.
Do it right:
Stand with legs wide holding weights, or leave weights on the floor for the modified version. Squat to put the weights on the floor - back straight, head up and shoulders back, making sure to send the hips back and down. Holding onto the weights, step or jump the feet back into a wide-stance plank. Hold that position or put the knees down (modified) and alternate a row on each side. Jump or step the feet back in a wide stance, squat very low (again, back straight, hips back) to pick up the weights as you stand. Repeat for 1-3 sets of 8-16 reps.