I use Kate as well. Kate's simplicity is its biggest feature. It doesn't get in your way. (This is of course highly subjective opinion.)
Kate includes a Python code browser plugin. But it isn't useful IMO. No automatic updates when you change the code/view. Also when you update, the whole tree is collapsed, and you have to expand it again yourself. Too many clicks.
Instead, I use the Source Browser plugin that comes with Pâté. It does cause Kate to freeze temporarily sometimes, but no crashes or anything of that sort so far.
Shameless blog plug: more on using Django with Kate (Pâté)