With a draft of 3'6" that should be do-able. However, you will need a long steep ramp, and possibly an extendable trailer tongue. I would scout out the ramp before you drive into the water. Make a mental note of where in ends under water so you don't drive off the end with the trailer.
Launching such boats from a trailer is nothing compared to loading them back. Guide poles on your trailer will help a little. Ramp has to be steep, long, and EVEN (smooth and not tilted). I would not like to do it more than once or twice a season.
Your best solution is a trailer hitch extension. This lets you really sink the trailer deep to get the keel to float off. My extension gives me almost 17 more feet of tongue length. Also, if there is a pier alongside the ramp, get you a solid pole and prod the ramp surface as you walk outwards on the pier (towards the deeper water). Find the point where the concrete of the ramp ends (soft muck or sand under the pole end) and there is often a "Cliff Hanger" there. You dont want your trailer wheels to hang over that ledge, ever!!!! Then measure the water mark on your pole and determine is the ramp adequate for your launch requirements. I count how many vertical pier posts there are at the deadly ledge, so I never go past the 7th post with my trailer tires when I back in. Be observant, at my marina there are 3 parallel ramps and each has a slightly different angle built in on purpose. I use the steepest ramp to get my keel deep much sooner. Saves me about 6 feet of trailer submersion compared to the other ramp on the opposite side. It will feel weird at 1st but its easy once you get familiar w your local launch area. I have only used one marina since I built my trailer, so I would have to do it all over if I moved to another town. Good luck, that boat has a very interesting design quality to it.
My boat draws about 3 feet with a shoal keel and it's always exciting trying to launch and recover it. I would suggest a tongue extender. It's nice to have it float off with out it sliding. Make sure the ramp is long enough and don't just take someones word! At the end of last season I was hauling my boat out and the Marina said the ramp would be plenty long enough. It supposedly went into the water for another 50 feet. It didn't and it's not easy getting the trailer back once if dropped off the edge!