My kids were SUPER heavy sleepers. Slept through fire alarms, house alarms, dogs barking, you name it. My boys were around 8 before they could make it through the night. My 9 yr old daughter was JUST able to stay dry at night. She wore pull-ups and on occasion, I didn't know she was out, so she would have to wear underwear to bed. Each time, she wet the bed. So, I knew she wasn't ready. We even purchased the WetStop alarm that we had used for the boys (non-consistently, really). We hadn't started to use it, yet (would have to work it for ME to hear the alarm, since my daughter would not be able to wake for it. I kept putting it off, since I like my sleep...LOL!) Anyway, last weekend, we ran out of pull-ups again. She went to bed and woke up dry. We were cautiously excited. I got more pull-ups (she begged- just in case). I told her we weren't going to use them until she had a "wet" morning. She never did!! Low and behold, she has been dry for more than a week, now. It was just her body finally being ready.
I would say that you could put her to bed with underwear on and see what happens. If she's not ready for that, wait. She should really be on board with the process. For my daughter, on the nights we ran out of pull-ups, I would lay a fleece blanket or large towel under my daughter. I would also lay out an exra pair of pj's and underwear. That way, if she wakes up wet and wants to just pull the blanket/towel off and change, then go back to bed. At 3 1/2, she may want "mommy" to help, but it's an option.
See what your daughter is ready for- if she wants to try to wear underwear at night. She may be all for it, or she may not feel comfortable, yet. There's no rush at this point. I wish you the best of luck! :)