The thing is, if someone ever plagiarizes you, it will be very easy to prove that they did so because you will have the date stamps on your own work on your blog to provide as evidence.
For example, you might have written a piece and posted it to your blog on the date of January 4, and this person might plagiarize your piece and post it to their blog with a date stamp of January 23. Date stamps don’t lie, and the fact that yours was earlier helps prove that you wrote the piece earlier, and therefore this person plagiarized you.
You can also email Tumblr Support and provide them with links to your writing pieces and date stamps, and compare them to the date stamps and plagiarized pieces of the other person. Tumblr Support, if given enough evidence, and generally the dates/links are enough, will remove the person’s blog for you.
You can also get a Creative Commons license for your blog, which helps prove that you retain copyrights to your work.
So you have several ways to protect yourself and your writing against plagiarism.
I would go for it! Sharing your work on your blog can be one of the best experiences you’ve ever had.