In this case, the first sentence is more natural.
In most cases, the first sentence suggests that the person has an inability to do the task. Big dogs are hard to clean, and she is old, so cleaning them is too hard for her.
On the other hand, the second sentence suggests that the person shouldn't or doesn't want to be doing the task (because of the reason). In this case, it suggests that being old makes the woman 'too good' to be doing such a task (?). As such, it doesn't really make sense.
With that said, it is far from uncommon to see both constructions used for both uses.