What forms would I need if my spouse and I both agree on filing for a divorce and have no children or real property together but still have 9 months left on our apartment lease?

It depends on the intent of your agreement and how you word it in the final order. 
If he pays half the rent as part of the property division or a debt of the community, then you want the final order to reflect that this is a property issue.
If he pays half the rent as spousal support, then the final decree needs to reflect the same.
Before you decide which one to include, at least visit with a divorce attorney to decide the best wording for your situation.  If you word spousal support incorrectly, then the funds could be considered income, and therefore potentially taxable.  However, if you word it as property division/debt division, then it is not taxable. 
You don't have to have an attorney to handle your divorce.  More and more county clerks are posting basic online forms that you can use to get started including an original petition and a final decree.  Some counties also offer legal clinics to help people with the forms.  So... call your local district clerk to see what resources are available.  If this is not available.... then visit with an attorney to have them at least look over your forms and make sure they are worded to reflect what you want to accomplish.  Many attorneys will do this for an expensive fee.  Most people don't have their forms reviewed and usually end up make more costly mistakes in their legal documents.  A bit of work on the front end can save a great deal of grief on the back end.