The information leaflet on Rent Supplement can be found at the end of the following web page:
[broken link removed]
If you follow the link on the page to the Dept of Social Protection website, you can get information on the maximum rent limits that will apply to your family size and location.
As you have been renting for over 6 months, you may have an entitlement. Bear in mind that while you may be allowed to continue renting your current property, the maximum rent limit for one adult and one child is €930 per month in Dublin and lower than that in other counties so you will probably have to renegotiate the rent in order to qualify. You may have been granted the Rent Supplement for the high rent because of the joint incomes.
Your partner would be unlikely to get Rent Supplement for your current address for that amount of rent - he would have to get somewhere cheaper before being eligible. As he's been renting for over 6 months, he may qualify.
You should both apply to go onto the local authority housing list.