Australia - Weather in Later March & April

The weather should be fine for all of your proposed destinations, and in particular that's actually a very good time to visit Tasmania.
The concern would be with regards to your trip north to the Reef and Daintree. Northern Queensland doesn't come out of "The Wet" until around the end of March, so I'd suggest delaying your excursion up there as far into April as you can manage in order to avoid possible disappointment.
My suggestion would be to bring the jacket. Better to have it and not need it rather that the other way around.

Thanks Robert. Our tour is April 6-15. I don’t have any control over the dates. I agree that it’s better to have something with me I may not need than to need it and not have it.

We have been to Australia twice, both times March-April and found it just fine. We didn't go to Tasmania.

It was still hot in Perth, Darwin and Cairns.

Melbourne's weather tends to be very changeable due to the proximity to the ocean, but also being close to higher inland temps. I have visited in March with 20 degree changes in temp between and even within days. (Not unlike Chicago....) I traveled with lots of layers, and needed them all! A packable jacket, especially if smaller, might be a great addition.

One of my GBR snorkel excursions was disrupted in mid-May due to an offshore cyclone. All worked out, but we left several hours later than planned. Point is - I had picked May for the visit as less likely than March or April for storms and still was (mildly) impacted by one. Can't control the weather!!

I've taken to traveling most places with a rain jacket that doesn't shout "Raingear". I wear it as a light jacket when it's cool and I'm prepared for rain. I find that historical averages have a way of not being accurate for my trips and current forecasts always seem to change between my departure and arrival and on-the-ground time. I'd rather be prepared!

Andrea, you should be OK for those dates in April. It probably helps in this case to be on an organized tour so that should any weather related issues arise you'll have an extra layer of security. As was mentioned, not only is it the tail end of the wet but it's also tropical cyclone season into May.
You have a great itinerary mapped out - You're going to love it.

Thanks everyone. I will go prepared for anything and hope for the best.