Yes and you can cut the factor ears off your current bucket buy a SSQA plate to weld on it. Good as new. I did this on my LA463. (Same style loader as yours just earlier version) Look around your area I found a place in Denton NC that makes all kinds of SSQA pieces and they sell the plates for 50.00!!! I bought three for that price. Dad's L3800 has the LA524 and now we can share buckets and pallet forks.
Be careful with SSQA buckets, as most are designed for Skid Steers, and they can be too heavy.
And most SSQA implements will be heavy and require more hydraulic flow or capacity then your tractor can put out.
Although it may "fit," it's not a guarantee that it'll work like you intended. Just take weights into consideration when you're choosing attachments and you'll be fine.
On a side note, there is a difference between SSQA, the old John Deere QA, and larger QA connections. Generally speaking, the SSQA (Skid Steer Quick Attach) and Universal Quick Attach are synonymous.