Is this pure speculation or would the IQ of ET be around 300? I read some scifi works have stated that the IQ of certain characters were this and that, was there anything like that for E.T?
No, an IQ of 300 is undefined, because the scale does not go that high. The IQ as per definition is calculated so that over a specific population, age group, etc it has a mean of 100 and a deviation of 15. This means you can not use this measurement to measure the intelligence of a non-human (or even of a human not within the age group of your test)
Popular "internet truths" such as a cockroach or a pocket calculator or a horse (or a non-human fictional character) having an IQ of X are all incorrect and have no scientific basis.
To measure the intelligence of E.T. you have to create a different metric, the IQ score system can probably not be used. Even if you used it, it is impossible to get a score of 300 with any notable test currently used. You have to create a specific test just for this purpose, which you would need to call something else, not IQ.