Well, yes and no. You have 1 GB of internal storage. That will never change. The deal is that you can only use a set amount of that 1 GB for apps and data. For an in depth explanation, read this
thread and this
thread. Without going into that much detail, though, a majority of that 1 GB is partitioned like this:
/system – 350 MB
/data – 430 MB
/cache – 160 MB
/data is the only partition you can actually use for apps and data. So, to answer your question, you can make that /data partition larger or you can move all apps to the sdcard. Both of those options do require root, though, as you suspected.
Resizing the partitions is much more advanced, though, and is not as simple as just installing an app. Read this
thread for information on how to do it. I wouldn't recommend this method unless you are very comfortable with all the steps. Also, heed all given warnings. Whether you have a custom or stock ROM, make sure you leave yourself enough space where it needs to be.
A potentially simpler option is Darktremor Apps2sd
aka a2sd. It is not the same thing as froyo apps2sd. You can read all about how it works and how it is different in those first two links above. Basically, it will move all apps from internal storage to the sdcard. This requires:
1) A custom ROM (more specifically, a modified boot image, but save yourself the trouble, and use a custom ROM that already has it done), and
2) A fast enough sdcard.
You would likely notice a lot of lag with opening and using apps if you were to use a2sd with the stock card. You'd want to use a higher class card, that is known to actually have transfer speeds at that rating (don't get a cheap, high class card; most of them aren't actually that fast).