What a horrible boss you have. Nobody expects to have to share everything with their boss, but you don't want to go full cloak and dagger either.
One of my team told me in her 121 this week that she had an interview externally this week. She didn't mean to tell me, it sort of iust came out as we were discussing how well she was doing. It prompted a whole discussion about her ambitions (most of which I was aware of and was supporting) and how she's desperate for more room and progression. I just had no promotion to give her.
As she was what businesses can refer to as a "flight risk", I spoke to my manager and a job (promotion) that my manager had that neither me, her, or my team member considered to be a role she could do is now looking likely to be something she is applying for and could actually do now we've all thought about it.
My boss said, we will try to keep her, but it must suit our cosny too, so if we can't keep her, then we have to support her to spread her wings, even if that means for another organisation.
I would suggest that if you're unhappy, a year is enough on your CV, I had a job that I knew was a mistake after a month, but I stuck it out for a year for the sake of my CV, it was hell. If you're unhappy, just start looking, but be careful about letting your boss realise, book a half day holiday etc. It's none of your boss's business.
You're right, you've no rights legally until you've been there for two years, so dont waste another year there. Find a company that deserves you.
When asked in interviews and on forms why you're looking for a new role, refer to the current company's size and how you feel that progession options are limited. That's perfectly acceptable.
Also, I've had a harder time working for small companies, bigger organisations have been much better. Such as, small companies often don't have a HR department, the MD usually wants to micro manage everything and the benefits are rubbish.
Good luck OP.