If a creature has double strike and deathtouch, does it kill a creature in the first strike step and still deal damage again?

Double strike (CR 702.4) means a creature deals damage in both the first-strike combat damage step and the regular combat damage step. Deathtouch (CR 702.2) means any amount of damage that creature deals is enough to destroy the defending creature.

During the first-strike combat damage step, the attacking creature with both abilities deals its damage. Because of deathtouch, even 1 point of damage is lethal (CR 702.2b). State-based actions then check at the end of that step (CR 704.3), and any creature with lethal damage marked on it is destroyed — before the normal combat damage step begins.

So in practice: yes, the defending creature is almost always destroyed after the first-strike damage step. The attacker then still deals its damage again in the regular combat damage step, but there is usually no target left to receive it.

This combination is especially powerful because the attacker can kill the blocker in the first step and, if it was also blocked by a creature with indestructible or regeneration, the second hit still matters. It also means a small creature can kill a much larger blocker in the first step and take zero damage in return if the blocker had normal strike.

Example: A 1/1 with double strike and deathtouch blocks a 5/5 with no special abilities. In the first-strike step, the 1/1 deals 1 damage — lethal due to deathtouch. The 5/5 is destroyed by state-based actions before it ever deals its 5 damage. The 1/1 survives unharmed and deals its second point of damage in the regular step to nothing.