Yes you can just replace one of the struts on your car and then replace the other strut later.
Struts are best replaced in pairs at the same time so that you can get your wheels aligned properly and have even tire wear.
But if all you can afford at the time is to replace one of the bad struts that is bad then you can do so.
I've been poor myself and had to replace one strut and one shock at a time but now that I can afford too I replace both struts at the same time when needed.
Struts should last over 100,000 miles or more and when your struts go bad your tires will start to wear out unevenly.