Calendar

Edited to add a couple of columns which are probably needed

See if this works. I'm assuming that FY19 begins on the 01/10/2019 and ends on the 30/09/2020.
Create a new column in your fact table using:

Quarter Start Date =
VAR QT =
    VALUE ( RIGHT ( 'Table'[Quarter], 1 ) )
VAR MNTH =
    SWITCH ( QT, 1, 10, 2, 1, 3, 4, 4, 7 )
VAR FY =
    IF ( MNTH = 10, 'Table'[Year], 'Table'[Year] + 1 )
RETURN
    DATE ( FY, MNTH, 1 )

 Now create the calendar table using:

Calendar Table =
ADDCOLUMNS (
    CALENDAR (
        MIN ( 'Table'[Quarter Start Date] ),
        MAX ( 'Table'[Quarter Start Date] )
    ),
    "MonthNum", MONTH ( [Date] ),
    "Month", FORMAT ( [Date], "MMM" ),
    "Year", YEAR ( [Date] )
)

 Add a column to the calendar table for the FYQ using:

FYQ =
VAR FY =
    IF (
        'Calendar Table'[MonthNum] < 10,
        'Calendar Table'[Year] - 1,
        'Calendar Table'[Year]
    )
VAR FQ =
    SWITCH (
        TRUE (),
        'Calendar Table'[MonthNum] > 9, "Q1",
        'Calendar Table'[MonthNum] < 4, "Q2",
        'Calendar Table'[MonthNum] < 7, "Q3",
        "Q4"
    )
RETURN
    FY & "FY" & FQ

Add a FY Quarter period using:

FY Qarter Period =
VAR FQ =
    SWITCH (
        TRUE (),
        'Calendar Table'[MonthNum] > 9, 1,
        'Calendar Table'[MonthNum] < 4, 2,
        'Calendar Table'[MonthNum] < 7, 3,
        4
    )
VAR FYPeriod = 'Calendar Table'[Year] * 100 + FQ
RETURN
    FYPeriod

And a order column for the fiscal year to use in measures to reference other periods.

Order = 
RANKX('Calendar Table', 'Calendar Table'[FY Qarter Period], , ASC, Dense)

Add a FY Number:

FYNumber = 
IF('Calendar Table'[MonthNum] < 10, 'Calendar Table'[Year] -1, 'Calendar Table'[Year])

and FY Column

FY = 
"FY" & RIGHT('Calendar Table'[FYNumber], 2)

The FYQ and FY can now be sorted by their respective numeric columns to be used in visuals.

 Create the relationship between the date fields:

Now you can create measures along the lines of:

Sum Sales Previous Quarter =
CALCULATE (
    [Sum Sales],
    FILTER ( ALL ( Calendar ), Calendar[Order] = MAX ( Calendar[Order] ) - 1 )
)

I've attached the sample PBIX file