First, be very careful about picking out a wheelchair. If the Q6 3 works for your situation, then it would be fine. But, don't let the wheelchair folks talk you into a wheelchair that does not suit your needs.
Second, your Lincoln Nautilus will barely be able to haul the wheelchair on a platform attached to the rear. To do so, you will need to have a receiver installed (if one did not come with the vehicle). Then, you will need to mount the platform on the receiver. The platform will probably weigh between 50 and 100 pounds. Finally, you will need to put your wheelchair on the platform. Your wheelchair is around 400 pounds, more by the time you put a few extras on it. So, you will be have a total of about 500 to 600 pounds of weight hanging off the back end of your vehicle.
Your Nautilus has a maximum allowable tongue weight (how much weight can be on the receiver) of 600 pounds. You will be carrying close to 600 pounds, which will not be as stable as a trailer. Those 500 to 600 pounds will be bouncing around a bit as you drive. Unfortunately, car manufacturers give optimistic numbers for towing capacity and maximum allowable tongue weight. Typically, they spec those with half a tank of gas, one 150 pound occupant, and sometimes no spare tire.
It is amazing how rapidly the maximum allowable tongue weight drops as you add passengers, gas, and cargo. The only way to know whether or not you are in spec is to load the wheelchair onto the vehicle and then weigh it on a multi axle truck scale (available at most truck stops). Once you know the weight on each axle, you can look up the maximum allowable weight for each axle and see if you are within spec.
Could you haul a wheelchair on a platform off the rear of the vehicle? Sure. Would it be safe? Maybe. Would it be wise? No. Here is why.
Water is the enemy of power wheelchairs. You don't want to expose the wheelchair to rain, snow, etc. as you drive around. I don't think it is practical to try to cover it in a way that will ensure no water gets to the electronics.
Also, going with a rear platform for the wheelchair is a temporary solution. Eventually, your PALS will not be able to transfer from the wheelchair to a passenger seat. At some point, you will need a solution where your husband rides in the wheelchair. Eventually, you will need something like a wheelchair van.
Rather than spending money on a marginally safe (or unsafe), temporary solution, I encourage you to bite the bullet now and consider getting a wheelchair van of some sort.
Now, with all that said, I started with a set of eight foot long suitcase ramps that allowed me to load the wheelchair into the back of my SUV. It barely fit, but it did fit. It is so impractical to do that we have only done it twice. We use a wheelchair van.
If considering a wheelchair van, get the wheelchair first. Not all wheelchairs fit into all vans. Be sure to try loading the wheelchair into the van before you commit to buying the van.
Steve