Yes, they're available. Private taxis are easily available during that time and so are shared ones.
There are plenty of private taxis available both outside the NJP (New Jalpaiguri) railway station and Bagdogra airport. Negotiate the rates and drop point prior to boarding the vehicle, it is advisable to take one from the Pre-Paid taxi counters. Usually takes about 3hrs to reach Darjeeling.
There are two places from where you will get shared jeeps for Darjeeling - Outside NJP(New Jalpaiguri) Station and next to Siliguri Main Bus Stand. Shared jeeps have 10seats and you'll have to wait until all of them are occupied, which can stretch up to 30-45min in low seasons. Shared Jeep fare is around 150rs from NJP and 130rs from Siliguri Bus Stand up to Darjeeling. Takes about 3.5 to 4hrs
Remember the taxis will drop you at Darjeeling town center (i.e. either at the Chowk Bazaar stand or at Clubside Taxi stand next to Gandhi Road police point).