AFAIK you need an EPA licence and they will have to do an audit on the site in case it pollutes the local water supply. It is not as simple as just filling in a hole. If you do get a licence you should make a fair bit of money out of it.
less than 5000 tonnes and the Council can simply grant permission. Probably best to get on board with someone in the council as most council's would be happy to entertain any extra waste facilities.
Call a few land fiull sites like the one you are looking to open, tell them you have a site to clear and ask how much they charge per tonne and per load.
I called into a local "soil reclamation facility" Very fancy name for a tip. last year. If i remember correctly he was looking for €50 per load. After you get your planning permission and waste permit from the council (paying them some contributions) you'll also need to factor in the cost of a bull dozer or other method of moving the material. A hard stand area and wheel wash near the gate will make life easier.
Sounds a bit small for landfill if its only 5,000 tons, not worth developing it as a waste facility. Would you not be better off developing the quarry?