When to book?

I'd wait until you are a year out to book catering and cake. You never know if they are going out of business, change ownership, or the quality may drop. I think you can book photographer, but since you have so much time, I'd just look around, may be sign up for their newsletter and wait for a good deal.
Usually Save-the-Dates are sent out 6-8 months ahead and then invitations are sent 2-4 months. So yes 2 months is fine

I think it would be okay to book a photographer and catering now. October has become a very popular month for weddings and those vendors book up fast. My wedding is January 2022 and we booked the venue which includes all the food last month and we booked a photographer last week. We’re currently in the process of booking a dj, but once we have that booked we’re going to wait another 6 months or so until we start looking for other vendors. Also, some places have holiday deals right now. I found a photographer on Facebook that offered us 25% off if we booked before 1/1/20.

I booked my photographer about 2 years out for an October wedding. She made a comment that she normally doesn't book *quite* that far in advance, but because October was becoming so popular, she was happy to draw up a contract. I also locked in early pricing, which was nice!

For cake, the bakery I want said to not reach out to them until January 2020 (I'm getting married October 2020). I went to a bridal open house tasting event they had earlier this year, and that's when I asked.

It really depends. Some of the more in demand photographers in my area are booked up for 2021 and only taking 2022 & 2023 bookings at this point. I'd do it now... but I'm photography obsessed and had a short list of only 3 photographers I wanted for my wedding.

I think the next thing you should book is your photographer. It is 100% personal preference though. We booked our venue first, then our photographer, bartender, then catering (when we decided not to go with our venue's catering), DJ and then our cake.

Our wedding is February 29, 2020 and we sent our invites out on November 29, 2019 with an RSVP date of January 15, 2020. We plan on giving our guests until January 20th before we start calling those who have not responded.

Most say you should send your invites out 8 weeks before the wedding, but I think this is personal preference a well. I sent ours out earlier because I wanted time to get everything else ready like our seating chart, place cards, favors, etc. before the wedding.

I'd say maybe send yours out the beginning of August with your RSVP date for mid-September. That way you have a month to finalize all of your numbers with you venue and caterer.