If you change to another plan or another provider with better maternity cover, then you will not be able to use that extra cover for 12 months, so you cant move whne already pregnant.
However, you post does not make sense. You say that the cost could run into 1000's.
Private care by an obstetrician in any of the big Dublins hospitals will cost between 2.5K and 4K ( I think, it might have changed).
This is not covered by any private health insurance plan. If you plan to go private, you would always have to pay yourself. Even if you move to a plan with better maternity cover, the best you will get is about 800 of the fee paid and the private room paid. Anyway, you are not guaranteed a private room, depends on availability on the day - they cant plan advance booking very well in maternity hospitals.
Your plan may cover semi-private care. Let us know what plan is it, and someone may be able to help find out what is covered.
Good luck with the big event. Don't get too stressed about stuff like this.