Yes, as said, it is how much you download that matters, the speed is irrelevant.
What can be confusing is the fact they give you download speeds in Mb and download limits in MB.
To the untrained eye, it is easy to confuse them.
So to explain, the first bit - the range of speeds is what people get connected to the same exchange as you. They will know the connection speed you get and others who are in a similar location to you - so estimate it closer to 1Mb - which is either what you get or somewhat close. Other factors can alter this dramatically.
The speed of the connection is usually measured in Mb/s or Mbps which is Megabits (to keep it simple - let's say 1000 bits of data) per second.
When you download on your 1Mb/s or 1Mbps connection, you are downloading up to that amount per second (subject to the speed of where you are downloading from).
Let's say you download the full amount per second, you are downloading (again, I'll make these a round figure to simplify as a MegaByte is actually 1,048,576 bits IIRC) 1000Mbps or 125MBps (or 125MB/s).
Notice it has become MB (MegaBytes)rather than Mb. This is because there are 8 bits in a Byte (b for bits B for Bytes).
Generally, the amount you can download is measured in MB.
You've not said what your limit is but if you have a monthly usage limit of 10GB, that is (for simplicity) 10,000MB.
If you are downloading at 125MB/s, it will take you 80 minutes to use up your allocation.
Now it is not as simple as that because webpages are made up of text and graphics etc. which all have varying sizes, but at 125MB/s, most web pages will download within a few seconds or so.
So because you are not downloading constantly at the full speed your connection can manage, this then means it takes longer to use up your 10GB.
However, the more sites you visit and the more you download, the more this adds up towards your 10GB.
Things like music and video and TV use more bandwidth for longer because they are greater in size than text or pictures. However, as you've said you are only browsing, this just means it will take longer to reach your limit.
Your browser will cache (store) images, so if you visit this website all the time, you wont need to download everything again as it will see some things are stored in your cache so you've saved by not downloading again.
You might also be downloading Windows (gradual) or Mac updates (in one lump usually), which also add towards your limit.
My advice would be to carry on as you are.
The time to upgrade is when the cost of your current package, plus any additional charges, overtakes the price of the next package up, most of the time. The upgrade package will have a greater download limit and mean it will be longer before you hit the limit. Sometimes you can have a package, incur cost for downloading more than your limit, and it is still cheaper than the next one up, of which the next one up undoubtedly will cost you more each month guaranteed, you wont necessarily use it all each month and you certainly wont get a refund. Whereas, you would not necessarily incur additional charges every month with the current package.
Do not consider the speed of packages because if all you can get is 1Mbps, which is about the same as me currently, faster products wont make any difference.
It really boils down to how much you use it...