Another aspect of regeneration in Magic the Gathering?
Yes, combat damage is dealt simultaneously.

510.1. First, the active player announces how each attacking creature assigns its combat damage, then the defending player announces how each blocking creature assigns its combat damage. This turn-based action doesn't use the stack. A player assigns a creature's combat damage according to the following rules:
510.2. Second, all combat damage that's been assigned is dealt simultaneously. This turn-based action doesn't use the stack. No player has the chance to cast spells or activate abilities between the time combat damage is assigned and the time it's dealt. This is a change from previous rules.

Your regenerating creature will assign its combat damage if it survives to the Combat Damage Step in which it will deal damage (I.e. if the defending creature had First Strike, and your creature did not, it may receive lethal damage before getting to its Combat Damage Step. The Combat phase is divided into 5 steps.

Beginning of Combat Step
Declare Attackers Step
Declare Blockers Step
Combat Damage Step
End of Combat Step


510.5. If at least one attacking or blocking creature has first strike (see rule 702.7) or double strike (see rule 702.4) as the combat damage step begins, the only creatures that assign combat damage in that step are those with first strike or double strike. After that step, instead of proceeding to the end of combat step, the phase gets a second combat damage step. The only creatures that assign combat damage in that step are the remaining attackers and blockers that had neither first strike nor double strike as the first combat damage step began, as well as the remaining attackers and blockers that currently have double strike. After that step, the phase proceeds to the end of combat step.

If a creature is removed from combat before the Combat Damage Step, it will not assign or deal any damage. Setting up a regeneration shield is not one of the listed methods of removing a creature from combat.

it leaves play
it regenerates [CR 419.6b]
its controller changes
it stops being a creature
an effect removes it from combat