How well do you plan to secure this oxygen tank and the rest of the cargo in your trunk?
When I was a teenager, I worked for a balloon/entertainment company, and we were always nervous driving around with helium tanks in the car, and helium is an inert gas. We were nervous because an exploding (rapid decompressing, not catching on fire) gas tank is something to worry about whether the gas in the tank is a fire hazard or not. Now consider how much of a fire hazard oxygen is....
I wouldn't do it unless I took several precautions, including installing brackets or straps to hold the tank stationary and securing all other cargo in the trunk to keep it from hitting the tank when the vehicle's momentum shifts. I would also try to mitigate the risk of the tank being compromised in a rear-end collision by positioning it and the brackets where they are unlikely to take a direct or indirect impact from a collision from any side. I would also make sure you have a fire extinguisher in the car where you can get to it quickly, in a location other than the trunk.
I'm trying to contemplate a scenario where the benefits outweigh the risks, and I can only imagine a couple such scenarios, as in when running out of oxygen might be a matter of life or death. If this is one of those scenarios, I would want to consult an expert in oxygen transport.