My guess is I can broadcast it any time I want to, even a year later. But I just want to ask to make sure.
Yes you can. The only caveat is that if the fees go up, your (lower fee) transaction might not be included in a block ... or it could take a loooong time. You might have to contact a miner and pay him to include your transaction.
I read about one guy, who had an old signed transaction with a very low fee and he was having problems trying to get it confirmed in December 2017, when fees were very high....
He did succeed in the end