new job

Don't start a new job until after your vacation. Expecting a month off almost immediately will hurt your chances of getting hired. Use the last three months of being in your old job to do all the due diligence you can manage about possible new jobs. Research potential employers, see if there are any short-term certs you can work on, etc.

Actively make time for healthy distractions so you don't focus on being at the job you dislike during this time. Three months- in the grand scheme of things- is not a long time.

I would definitely be up front about it. I actually got my current position for being up front about something similar. I was going on a mission trip and told them during the interview that if I was offered the position I would need to take off for planned mission trip. Come to find out the manager is also a pastor part time and I really think that played into me being hired.

A weekend trip planned in advance is not hard to work around for a new employer...even a week seems do-able. But asking for a whole month off when you're new is just too much.

I would wait to even apply.

Landing a new job can easily take three months. Start searching now. If you find something you want, negotiate your start date to follow your holiday.