Are you planning to use TD for your index funds? That's what I do and I've been very happy with them.
Once your account is set up, yes, you can just sell the unregistered and transfer them into your TD cash RRSP account. At a branch, or with online banking.
Of course, depending on your income you probably want to put the $60,000 into RRSPs over 2-3 years, to reduce your tax burden for several years, unless you're easily able to max everything every year. But you can do TFSAs with some of it as well, if you haven't been using that room.
For the RRSP you'll want to transfer that. In my experience there's a transfer fee from $50 to $100 depending on the bank. (Can't comment on other fees there may be.) But paying this small amount has been well worth it, as you'll make that money back pretty quickly. You just get a transfer form from TD and they forward it to your mutual fund provider. You just transfer it in cash. So they sell everything, forward it to TD as cash. Then you buy e-series funds with it.
Presumably your financial adviser is commission based and works for one of the mutual fund companies? - Investors Group, Sunlife, etc. Yes, then they will object, and you should ditch him. No reason to pay the high MER on those mutual funds.