I do it myself for our nanny. Its not difficult once you've worked out how to use the HMRC software. The hardest thing was the getting my head around the tax/NI thing but it sounds like you may understand that already.
I would advise against farming it out because if they get it wrong you're still the one that's liable. I'd put the money towards sorting out a decent employment contract as when things go wrong or get complicated that's where you'll save yourself some pain not 30 minutes each month doing the RTI submission.
Oh, and I would start the RTI thing NOW because you can't submit anything until you have your account set up and it takes HMRC a few weeks to create it.