The exact formua is as follows (from the borderlands wiki):
All characters' base melee damage equals 20 × 1.13L, where L is the character's level. Thus, level 1 melee damage equals 22.6, and level 50 melee damage equals about 9014.7.
However that's not the whole story; it's changed by your buffs (and not all buffs seem to stack), badass rank, skills, etc. So the easiest way to find how much damage you do with your buffs is to go punch something. Melee damage is based on your level, and then increased/decreased based on the distance between your level and the enemy's level. Unfortunately I think Target Practice might be too far away to melee. You can melee Claptrap's hand if you can get him to High Five (it shows as a conversation option, which unlocks eventually), but I'm not sure how claptrap's level scales.
Probably the safest way to test melee damage is to find a bandit exactly your level and punch him in the chest, then watch the number that comes off. Hit an unarmored, even level target for the clearest idea of your base damage. Hitting resistant parts of an enemy ("armored" parts like helmets) does reduced damage, so try to hit something unarmored like the common Psycho.