I'd go for a diaper pail even if space is tight for you. I've been through it myself and the smell is really no joke - at 8 months old your daughter's producing a lot of diapers per day and they seriously start fermenting in a regular trash can. In my bathroom it sometimes got so bad that I had to open the windows. The Sangenic or similar models aren't super cheap, but the odor control is really effective. The cassettes with the multi-layer system work better than you'd think, and you don't have to take the diapers out every day like with a regular trash can.
As for the space issue - I get the problem, but I'd see if you can put the diaper pail somewhere else, like in the hallway or a corner in the bedroom. Or you could look at smaller models that don't take up as much room. There are also cheaper alternatives to the Sangenic that work pretty similarly. If you really absolutely have no space, you can try a regular trash can, but then you'd really have to be ready to take it out multiple times a week and use odor eliminators like spray - and that gets exhausting and more expensive in the long run than just having a diaper pail.