Honestly, you can try to work on her night time potty training, but at 3 1/2 her body may not be completely ready. At night their blader has to be mature enough and get used to holding it all night instead of a few hours. That can take a while. And the other posters may be right about her peeing in the morning, but that doesn't meen she is just laying there because she doesn't feel like going to the potty. She may not realize she's peeing until after it's on its way out. Pee in the morning doesn't have to meen that she woke and peed. She may be peeing and waking up because she's wet.
If she is close to being ready, then taking off the pullups may be a good insentive to get her use to the real feeling of wet clothes, sheets, and blankets. If all of it gets wet, not only is the wetness uncomfortable, but it also gets very cold and very dificult to sleep in. So, that could help give her that extra desire to stay dry. If you try that for several days and she's still wet most nights, then she probably is just not ready. Just remember, there are some kids that are just getting daytime potty trained at that age, so I don't think there is anything wrong with her weting at night or in the morning.
My daughter is almost five and she stays dry most nights, but she still has accidents sometimes. I just tell her that when her body is ready she will be able to stay dry everynight, and wake up when she needs to go.