No problem! Measure your bathtub (length and width and height to where your child can hold his/her nose and submerge). Mark that height and fill the tub to that point. Have your kid get in and go under. Mark the new height. Calculate the volumes by L x W x H in both cases. The difference is your child's volume! This was figured out many years ago by that famous Greek, Archimedes, who yelled "Eureka" and ran thru the town naked, or so the story goes.
greenprof2's answer is correct. But it might be difficult to calculate both volumes based on W x L x D (width, length, depth) since most bathtubs have sloped and curved surfaces.
I would follow the prof's instructions up to the last step and then measure the difference in water height and, if your bathtub is relatively rectangular at just this level, use that difference as D. So rather than
W x L x D2 - W x L x D1 (where D1 and D2 are the before and after depths)
W x L x (D2 - D1)
That might be easier.
Yet another way: don't use a volume calculation at all. Once you have the two marks and the child gets out of the tub, add water a gallon at a time until the tub water level reaches the higher mark precisely. Keep count. Multiply your number of gallons by 231 to get the number of cubic inches of water displaced by the child and therefore, the child's cubic volume.
Multiply the gallon count by 3.785 to get the number of liters.