You'll need a better CPU, GPU, more RAM, and faster storage, preferably an SSD. 0 A.D. might look like a game with tiny creatures and buildings on the screen, but they're actually 3D models, and every unit has its own AI. All of that takes quite a bit of CPU power and memory. I don't know all the technical details, but this game can be pretty demanding. However, the developers have done a good job of optimising it so that it can run even on older, low-end PCs.
You'll be fine playing single-player matches against AI, but if you're planning to play multiplayer, you'll need a PC that can run the game at a speed comparable to that of other players. Most multiplayer players have gaming PCs. If your PC lags, some of them will get annoyed and might even start a smear campaign against you.
I used to have a slower PC (I have a mid-range PC now, because I'm a poor guy), and some of the people who hated me back then still hate me. They kick me out of games, insult me, and so on.
I don't really care about them anymore. I just enjoy this game, and that's why I'm still playing. I've been playing it for almost a decade now, I think.