Medium Transport
Flight Crew Air Transport Pilot (ATP)
Distraction
Deviation - Speed All Types; Inflight Event / Encounter Other / Unknown
Flight Crew FLC complied w / Automation / Advisory
Weather
During the takeoff roll; I noticed that the wind was pretty gusty and centerline became exceptionally hard to maintain. As we rotated; I could feel the wind on the airplane and again noticed it was difficult to maintain the appropriate pitch and heading. Additionally airspeed began falling off; but I was unable to catch by how much. Shortly after takeoff; the wind shear alert went off. I asked for full power and pitched for the V-bars. We seemed to recover out of the wind shear within a few hundred feet and at that point began to clean up on schedule. We received initial ATC instructions to turn; join the course and climb shortly thereafter and feel like we were a little delayed/sloppy in following those instructions as we were still recovering from the wind shear.Just after the wind shear aural came on; Tower gave us the handoff to departure. There was a lot going on; but I feel like it may have been more prudent to tell the Tower to standby until we were fully recovered.The Captain instead took the handoff; simply stating 'we had some wind shear'; and then switched to departure. I feel we got distracted with that clearance rather than concentrating on the wind shear cleanup. Shortly after we got a climb; we both think we heard 15;000; but as we leveled the controller stated he thought he had given us a higher altitude. I think we may have mis-heard the instruction as we were task saturated. The controller did further state 'no worries' regarding the altitude. I'm not sure if that's because I realized we were task saturated or because he may have realized he had forgotten to clear us higher.
Flight crew experienced wind shear during takeoff roll and initial climb.