Have you pulled back a corner and are certain the pad is missing. Usually, the pad fails or disintegrates in high traffic areas if the carpet is not regularly cleaned. The dirt falls through the backing and acts as an abrasive to break down the pad.
I did a carpet pad replacement in the bedroom in my condo earlier this year. It took longer to move the furniture out of the room than to replace the pad.
If you are only replacing a 6x9 foot area with no seams, I would likely just replace the carpet and pad if I could find a usable pattern on roll at Lowes or Home Depot or a remnant at a dealer.
In either event, be prepared to vacuum up a lot of dirt and possible degraded carpet pad.
I have never seen carpet pad attached with an adhesive to the subfloor, but I have only pulled carpet and padding on concrete and chip-crete surfaces. Seams in the padding are taped with a special longer life pad tape, but I have seen packing tape used in a pinch.
I have used a cheap knee kicker (about $20 after discount coupon at Harbor Freight), a carpet knife, and a 4" heavy duty putty knife to remove and reattach the carpet to the existing tact strip. I used the knee tool to get slack in the carpet to allow lifting of the backing from the tack strip rather than "ripping it up" and tearing the backing at the edges.
I did need to trim about 1/2 inch on a 12 foot span when I reinstalled the carpet. I didn't pull the baseboards, and was able to neatly tuck the carpet under the existing baseboard using the putty knife.