If it were me? No, I would not do the Starlight Safari on the first night of my first trip to WDW. I would be tired from travel. I would want to get some rest and be ready to go to a theme park at rope drop (Early Entry if I were staying at a Disney hotel) the next day so that I would be there when the lines are shorter. You can ask in the Animal Kingdom thread how early in the morning you would need to leave the hotel, based on the parks you plan to go to and the method of transportation you plan to use. This would be especially true if my first trip was just 2 nights.
If I were to list the things I would try to do on a very short first trip to WDW, the Starlight Safari would be very far down on the list.