@Ross at Play
As a point of technical trivia, there are times I would insert a comma between a word being used twice in a row, even where a comma is not usually allowed. That seems like the lesser sin if readers might attempt to interpret the sentence assuming the author made a typo, or they might not "see" the duplicated word because their brains assumed it was a typo.
I've done that before, but in this case, it clearly doesn't belong as "I gave her, her own space" sounds terrible.
Actually awnlee's suggestion seems the most practical, simply insert the person's name instead of the more generic "her", so it'd become "I gave Dawn her own space". That eliminates any confusion, without taking away the initial impact of the sentence.
By the way, who died to get the hearse in the title?
As explained in the first entry, the duplicate her made me think of multiple "hers", which made me think of "hearse[s]", since "hers" is generally interpreted as being the possessive form. As far as who died, clearly the second her, since the first lives on as Dawn. :D