Yup, you can def ask now. Alternatively, you could let her know now and just submit the request closer to when you’ll be submitting. If they know you well enough to write a LOR, they shouldn’t forget over the summer. Don’t worry about dates
I'm in the same place! I'll finish the course mid-May. So far things have been going well, but I'm concerned June is too soon. I'm putting in long hours at the moment, so I may see how I'm doing Mid-May (deadline for changing test dates)