I wouldn't sell your 06 short. We used to have a member (he passed away) who hunted everything with 30-06. He used to hunt antelope in Wyoming every year for almost 20 years and only used his 30-06. As part of your preparation for hunting big game, you should take your 30-06 out to the range and experiment with different bullets at different ranges. If you go to the top of this forum (Big Game Hunting), you'll find a sticky topic titled "Wyoming Antelope." Scroll down to the last 2 posts from Big Uncle and Bocajnala (one of the mods). I've included a link below to big Uncle's post and his field notes from several years of hunting antelope in Wyoming. Big Uncle said his average shot was very close to 200 yards. Jake (Bocajnala) said his long shot was 267 yards. In Jake's opinion, he thought an antelope hunter should be prepared to shoot up to 300 yards.
Your 30-06 rifle is capable of making shots like that. If you practice and get good at shooting at those ranges. Depending on where you zero your rifle (say 150 yards+), you're going to shoot 1-2" low at 200 yards and 8-9" low at 300 yards. You would still have over a ton of energy at both ranges and enough speed to reliably open just about any bullet you choose. You're going to want to buy points in Wyoming but with only a point or 2, your chances for getting a good tag improve quite a bit. That would give you a couple years to hone your hunting skills, get proficient at shooting your 06 up to 300 yards and save for your hunt. Keep asking questions and some of the guys who've hunted antelope will come along to answer them. In the meantime good luck.
Wyoming antelope