Plugging in my dishwasher and water filter to the same outlet with an extender

Don't use an extender!

Assuming an extender is some sort of little 3-to-1 (or similar) gadget to just "make extra outlets", those are not normally recommended for (a) permanent use, (b) hidden use or (c) high power use.

• Permanent Use - They get forgotten and they are an extra point of failure since they are just "hanging around" so they are not really attached in any permanent way.
• Hidden Use - Since they are not really attached in any permanent way (screwed in), they can come loose without you knowing because they are hidden inside the sink cabinet. Loose is worse than out. If an extender or anything else comes totally out, you research the problem and plug it back in. But if something is loose then it can lead to high-resistance connections, arcing and other problems which can lead to fire.
• High Power Use - The first two problems are multiplied when dealing with high power use (e.g., dishwasher when running the heating element), plus many extenders, extension cords, etc. are actually rated in the fine print for only low power usage. Not a problem (generally) for occasional use, but for frequent and hidden usage, this is a big problem.

The proper solution is to replace a single receptacle with the more typical duplex receptacle, or if this is already a duplex receptacle (e.g., split circuit - top = disposal, bottom = dishwasher) then add a new duplex receptacle next to it. If you do not need a new circuit (which depends on total power requirements - separate question!) then this should be a fairly straightforward upgrade, at least if you have easy access to the existing receptacle/box.