Hello Bunbunb, I think this is up to your preference. For me, my wedding day is same as yours but I have already approached a solemniser and she has confirmed she will put in her schedule to block out the date for me hehe.
It is better to have someone rather than last minute panicking cos can't find a solemniser right? Furthermore if you have criteria that the solemniser must be a male or female, bilingual etc, better to start looking early. Not forgetting some solemnisers want to be transported to your venue, you also need to make early arrangements for that!
Hope this helps!