First of all you can't file a tax return for 15 months.
You'll have to file an annual return for 2015 - 1/1/15 - 12/31/15
Then if you want to switch to a y/end of 3/31, you'll have to file a short period return for the period 1/1/16 - 3/31/16 & then you would go to 4/1/16 - 3/31/17 as your next return.
As far as changing from the Cash Basis of Accounting, you need to file Form 3115 and comply with all the instructions that basically require computing the adjustment to make the switch and then depending upon the results, which may be a "pick-up" of income, that adjustment may be spread over 4 years. This is all in the detail instructions to the 3115.
Here's a copy of a summary of certain of the main requirements related to the change:
Form 3115 you file this form to request permission to change your accounting from cash to accrual method of accounting. You must follow the prescribed procedure so you don’t inadvertently let income or deductions drop between the cracks—and so you gain some special benefits afforded to people who “play by the rules.”
Note that normally with cash-basis accounting, a firm delays reporting income and therefore delays paying taxes on the delayed income. What this means is that this “would have been reported earlier” income drops between the cracks when you switch from cash accounting to accrual accounting. The IRS watch carefully for this. Further, what your Form 3115 with its Sec. 481 adjustment (the cash to accrual adjustment) does, is report this amount. As stated above, if the 481 adjustment results in additional income, you get to split the amount over four years. If the 481 adjustment is a cut in taxable income, you can report the entire adjustment at once.