I drained my pool for a couple of weeks to change the water, clean the
pool surface and replace the pump. Today as I started filling it I
noticed that a 4" chunk of plaster under the skimmer inlet had fallen
away to reveal the gunnite beneath.

Do I need to stop filling the pool below the plaster hole to prevent
water from getting inside, and behind, the plaster? Or is this a
repair I can deal with another time and I can fill the pool up to the
top for now and then just drain the pool below the hole when I'm ready
to fix it?

How hard is it to patch the plaster, is this something I can do myself
or do I need to have a pro do it?

HamNCheese writes:

Do I need to stop filling the pool below the plaster hole to prevent
water from getting inside, and behind, the plaster?

No, don't worry about that.

Or is this a
repair I can deal with another time and I can fill the pool up to the
top for now and then just drain the pool below the hole when I'm ready
to fix it?

Yes.

Assuming there's no crack in the shell that's going to leak water, in
which case you could just do a quick and sloppy patch to stop that.

How hard is it to patch the plaster, is this something I can do myself
or do I need to have a pro do it?

Patching with "cold joints" has from ancient times been nearly
impossible to screed and finish properly, but if you're willing to pay
for diamond polishing tools, you can do a perfect job of it by putting
on too much plaster and polishing off the excess. See my description
at:

http://www.truetex.com/pool.htm

Thanks. From what I've read doing a search, there are actually
plaster mixes I can use to patch it that will set underwater, so I
won't have to drain it at all. This is a pool that is in need of a
replastering in the next year or two anyway, so I'm not too concerned
with how it will look.

HamNCheese writes:

From what I've read doing a search, there are actually
plaster mixes I can use to patch it that will set underwater, so I
won't have to drain it at all.

Imagine that. Let us know how well it works. Hard enough to work plaster
when conditions are ideal.

By the way, all portland cement products will set under water, including
ordinary pool plaster.

This is a pool that is in need of a
replastering in the next year or two anyway, so I'm not too concerned
with how it will look.

It's not just a matter of looks. A rough patch will just collect algae and
crud, and will be as bad or worse than no patch at all.