I'd suggest you either work with your agent (or find another one) or do it yourself. There's no benefit and probably a chance of confusion if you try to submit them in parallel (plus duplication of any assessment fees).
You don't mention the circumstances of your application but here is my advice:
- don't submit your documents yourself, it will just create confusion which could cause a delay.
- if you have already paid your agent, then you have every right to demand prompt service. If they are a MARA-registered agent I think there might even be a contractual obligation as to how long they can take to do things. Find out. And in the meantime, call them up and ask what's going on, and remind them that the fees go up from 1 January so they need to submit before then otherwise it will cost you more!
Like any other service that you pay for, you should get what you pay for.
- if you haven't paid your agent and your case is pretty straight-forward, consider doing it yourself online. We applied for our Partner Visa in September and I found the online process surprisingly easy. Not to mention a MASSIVE saving on agents fees.