I've never hunted elk, so you might want to double check with somebody better acquainted with North American game, but based on their size I'd feel better with a few more pounds.
I'm not saying you can't hunt elk with a 45# bow, but I prefer to have a bit more power just in case. My hunting bows start at 60# (I only shoot traditionals) I really like that draw weight, it's pretty fast from a well designed recurve or longbow and coupled with some well chosen arrows and broadheads it performs well on anything around here. For big critters that hit back, I go a bit heavier.
Don't go rushing out to get a 80# bow, though. Hitting what you aim at and being comfortable with your bow is much more important than getting more weight. Practice, practice, and then practice some more. Shot placement is everything. A well placed arrow from a 50# bow always beats a miss with an 80# one.
Invest in good arrows and broadheads, no need to get the most expensive super high tech stuff, go for the tried and tested. Play around with broadhead weights to get the most out of whatever draw weight you settle for.
Did I mention practice? One of the great things about archery is that arrows can be used over and over again, no expensive ammo to worry about.
Being a take down, the bow you bought gives you the advantage of using light limbs to learn and practice and a set with heavier draw weight to hunt with. I'm a big advocate of using a very light draw weight to learn. Consistency in your technique is of paramount importance if you're going to shoot recurves instinctively. Each time you draw the motions should be exactly the same, that way your brain can focus on hitting the target.
And remember the old saying "train as you fight", in this case it would be "train as you hunt". Shoot from different stances, try not to know the exact distance to the target and don't use FITA style targets. You're training to hunt, not to punch paper at the Olympics. Find something small, I use round red stickers about 1" in diameter (I've got some bigger ones for longer distances). Always use the same type of marker. Get used to it, and later on when you hunt just imagine your marker on the animal's vitals.
I think I picked up this "red sticker" technique from Jay Kidwell's book "Instinctive archery insights". It's quite good. I recommend it.
Sorry if this sounds like a bit of a lecture. It's not meant that way. I just want to share what worked for me. Like I said before, I'm no expert. I'm just an avid bow shooter.