Know nothing about suspension and steering, should I attempt?

Thanks to everyone who responded. I've been watching some YouTube videos on suspension and it's doable with my current tool set plus a rental from our local auto parts store. We don't have the same parts stores up here in Canada, but they do offer many of the same services. I am going to attempt this, then take it for a professional alignment.

Just to add some more detail why I want to do this. The car has been off the road since 1984. The PO told me he bought it from a guy who had to finally give up on the restoration, he apparently rebuilt the engine, transmission, had all the body work and paint done. We bought it non-running. The PO hadn't had time to put any work into it. My son and I spent the last 18 months searching for parts and asking for plenty of help here on FABO, thanks again to everyone for getting us to the point where we could actually drive it. Now we're shaking out the hidden things you can't see from a visual inspection. It's running great and making enough power to howl the tires at the lights. Last night we decided to leave the neighborhood and try it at highway speed. Not so good at 60MPH, the hood started shaking and it seemed like it all wanted to come apart. I think the 46 year-old suspension is a major part of that, but I'm also wondering if the missing fender braces play a part here too? How critical are these braces to the handling of the car?