Alright so if you want to get the ring, here's how you get back to the Undead Asylum. From Firelink Shrine, use the lift shortcut up to the Cathedral but instead of taking it all the way up jump out onto a stone ledge (this may be easier to see on the way down) here you'll be above the part of Firelink near Petrus. From turn right and go forward onto the grass nearby, go right to the edge and roll off in the direction of the moss covered stone arch. Walk up the arch into the interior of the ruined tower and then up the stairs to your left. Here you'll see a lootable corpse on the building beneath you, get it. Then you'll need to do the whole lift, ledge, roll thing again. This time however when you get to the stairs in the interior just keep going up till you get to a birds nest, stand in the birds nest and crouch as it prompts you too, then just wait
The ring is easy to get, as discussed above you only have to fight some hollows. However, be aware that when you enter the area that you fought the Asylum Demon in back at the start if you walk out into the middle of the courtyard, it will give way and you'll be forced into a boss fight, after taking a good chunk of fall damage, which is unavoidable, so go round the sides if you wish to avoid this for the time being. Well worth fighting the boss at some point though, for the reward as well as the sense of accomplishment.
All that being said, I tend to agree with Traveller that now you are down there, you might as well just power on through the swamp to the hilly looking area off to the far right from the bonfire alcove. There are two boulder dudes here, but frankly you can just run past them. The tunnel to the boss is here, you might as well stick around until you've defeated her now you're here. Reverse your hollowing and kindle the nearby bonfire for best Estus before you do so, and feel free to summon Man-Eater Mildred outside the boss fight (more for distraction than anything else) if you've already defeated her when she invades outside the bonfire - this only happens if you're human, so perhaps reverse your hollowing at the fire, kill her when she invades then rest again before being on your way to Queelag. Her presence in the fight isn't necessary though, she won't last very long anyhow, but the distraction, however temporary can be nice, especially when you've no idea what you're in for. You can come back with the Rusted Iron Ring later for exploratory purposes, it becomes very, very simple to travel there later on after a couple more mandatory story bosses. I would highly recommend exploring thoroughly once you do have the ring, you never know what you might find if you look hard enough...
EDIT: New comments while I was posting, seems like you've left the area, that sounds like the Undead Dragon in the Valley of the Drakes area. Pro tip, that dragon doesn't move very far, pepper it with arrows from afar if you have enough. Just so you know though past that dragon is two completely different areas, if you want Firelink, it's basically infront of you over some beams when you leave Blighttown.
This post has been edited by WinterPhoenix: 25 February 2017 - 12:57 AM